Force Converter

Convert between SI, gravitational, and CGS force units (newton, kilonewton, dyne, kilogram-force, tonne-force, pound-force, ounce-force, short-ton-force) with NIST-grade exact factors anchored to CGPM 1901 standard gravity.

Ovaj kalkulator još nije preveden na jezik Hrvatski.

Trenutno prikazujemo verziju na jeziku Engleski (SAD), dok ne dovršimo prijevod.

From

Value

lbf

Result

4.44822 N

1 lbf= 4.448222 N

Decimals

All units

Unit	Value
Newton (N)	4.44822
Kilonewton (kN)	0.00444822
Dyne (dyn)	444,822
Kilogram-force (kgf)	0.453592
Tonne-force (tnf)	4.53592E-4
Ounce-force (ozf)	16
Pound-force (lbf)	1
Short ton-force (US) (tonf (US))	5E-4

Ažurirano: 19. svibnja 2026.

Force converter. SI, gravitational and CGS force units with NIST-exact factors.

A force converter changes a value from one unit of force to another using exact factors anchored to the SI newton and CGPM 1901 standard gravity. So 1 lbf = 4.4482216152605 N and 1 kgf = 9.80665 N are definitions, not approximations, and every conversion in this tool is tagged exact.

What Is a Force Converter?

A force converter is a tool that takes a measurement in one unit of force and returns the equivalent value in any other supported unit. Every conversion in this calculator routes through a single base unit, the newton (N), using each unit's defined factor: 1 kilonewton is exactly 1000 N, 1 dyne is exactly 1 × 10⁻⁵ N, 1 kilogram-force is exactly 9.80665 N, 1 tonne-force is exactly 9806.65 N (= 1000 kgf), 1 pound-force is exactly 4.4482216152605 N, 1 ounce-force is exactly 0.27801385095378125 N (= lbf / 16), and 1 short ton-force is exactly 8896.443230521 N (= 2000 lbf). These are not engineering approximations; they are exact rational factors that drop out of three fixed values: the SI newton (1 kg⋅m/s² since the 2019 SI revision), the 1959 International Yard and Pound Agreement (1 lb = 0.45359237 kg exact), and the 3rd CGPM (1901) declaration that standard gravity is exactly 9.80665 m/s².

The single most-important fact about a serious force converter is the status of standard gravity. g_n = 9.80665 m/s² is not the measured gravitational acceleration at any particular spot on Earth (the real number varies from about 9.78 m/s² at the sea-level equator to 9.834 m/s² near the poles, dropping as low as 9.764 m/s² atop Mt. Chimborazo). It is an exact defined constant, fixed by the 3rd General Conference on Weights and Measures in 1901, that anchors every gravitational force unit — kilogram-force, tonne-force, pound-force, ounce-force, short ton-force — to the SI newton. Because g_n is exact, and because the 1959 IYP avoirdupois pound is exact (0.45359237 kg), the pound-force factor 0.45359237 × 9.80665 = 4.4482216152605 N is also exact, with zero rounding error. The same logic makes ounce-force exact (lbf / 16, where the 16 is a power of 2 that preserves bit-exactness in IEEE-754) and short ton-force exact (2000 × lbf).

This converter supports eight units across three families. The SI family (newton, kilonewton) is dominant in scientific publishing, modern engineering specifications, and every modern physics textbook outside the US. The gravitational family (kilogram-force, tonne-force, pound-force, ounce-force, short ton-force) is the legacy of pre-SI engineering practice and is still standard for US aerospace thrust ratings, structural-load specifications, automotive brake and clutch pedal forces, and gym weight plates. The CGS family (dyne) survives in surface-tension measurements, biomechanics, and older electromagnetism literature. The most common pair in everyday engineering is lbf ↔ N for any cross-border thrust, structural-load or test-bench specification; the most common pair in physics homework is dyne ↔ N; the most common pair in hydraulic and motor-torque catalogues is kgf ↔ N. All three are exact in this calculator.

What distinguishes a serious force converter from a marketing widget is honesty about which factors are exact and how many digits matter. Most online converters print 1 lbf ≈ 4.4482 N (4-decimal rounding) and stop there — introducing about 2.16 × 10⁻⁵ N of drift per pound-force, which accumulates to ~0.216 N over 10,000 lbf and ~21.6 N (≈ 4.86 lbf) over a 1,000,000-lbf rocket-stage thrust budget. Invisible for daily engineering, but it starts to bite at primary-force-standard metrology scales. This converter exposes the full 4.4482216152605 N exact value, lets you read up to 15 decimal digits (the full IEEE-754 mantissa), and tags every result with an “exact” badge because every supported pair in the force set is definitionally exact.

How to Convert Between Force Units

Every force conversion is one multiplication and one division through the newton. The general formula is:

y = x \cdot \frac{a_{\text{from}}}{a_{\text{to}}}

where $x$ is your input value, $a_\text{from}$ is the source unit's factor to newtons, and $a_\text{to}$ is the target unit's factor to newtons. To do it by hand:

1. Look up the source-to-newton factor. For pound-force, $a_\text{from} = 4.4482216152605$.

2. Multiply the input by that factor to get newtons. 1000 lbf × 4.4482216152605 = 4448.2216152605 N.

3. Look up the target-to-newton factor. For kilonewtons, $a_\text{to} = 1000$.

4. Divide the newton value by the target factor. 4448.2216152605 ÷ 1000 = 4.4482216152605 kN.

The same procedure works for every supported unit. Going from kilogram-force to newtons: 1 kgf × 9.80665 N/kgf ÷ 1 N/N = 9.80665 N exact. Going from dynes to newtons: 1 dyn × 1e-5 N/dyn = 1e-5 N exact (the classic CGS-to-SI conversion every introductory physics course tests). Going from pound-force to kilogram-force: 1 lbf × 4.4482216152605 N/lbf ÷ 9.80665 N/kgf = 0.45359237 kgf exact — a result that is mathematically equal to the avoirdupois pound in kilograms, because both pound-force and kilogram-force are defined as mass × g_n with g_n cancelling.

To use this calculator, pick the source unit from the “From” dropdown, type a value, then pick the target unit from the “To” dropdown. The result updates on every keystroke. Click the result card to copy it to the clipboard. Use the precision selector to switch between auto (6 significant figures), or a fixed 0, 2, 4, 6, 10 or 15 decimals. Auto-precision switches to scientific notation when the result is larger than 10¹² (one trillion) or smaller than 10⁻³, so converting a Saturn V first-stage thrust (~34,000,000 N) to dynes (~3.4e12 dyn) still renders readably. The “exact” badge appears next to every force result, because every unit in this set has a rational, definitionally exact factor to the newton.

Force Conversion Formula

y = x \cdot \frac{a_{\text{from}}}{a_{\text{to}}}

$y$ = The converted value, expressed in the target unit of force.
$x$ = The input value, expressed in the source unit of force.
$a_{\text{from}}$ = Factor that converts the source unit to newtons (e.g. 9.80665 for kgf, 4.4482216152605 for lbf, 1e-5 for dyne).
$a_{\text{to}}$ = Factor that converts the target unit to newtons (e.g. 1000 for kN, 9806.65 for tonne-force, 8896.443230521 for short ton-force).

The formula is a two-step pivot through the newton base unit. The factor table this calculator uses is sourced directly from NIST SP 811 Appendix B.8 and anchored to three exact upstream definitions — the SI newton, the 1959 International Yard and Pound Agreement (1 lb = 0.45359237 kg exact), and the 3rd CGPM (1901) declaration that g_n = 9.80665 m/s² exact:

Newton (N): 1 N (exact, SI derived unit; 1 N ≡ 1 kg⋅m/s²)
Kilonewton (kN): 1000 N (exact, SI)
Dyne (dyn): 1 × 10⁻⁵ N (exact, CGS; 1 dyn ≡ 1 g⋅cm/s²)
Kilogram-force (kgf): 9.80665 N (exact, CGPM 1901 × 1 kg)
Tonne-force (tnf): 9806.65 N (exact, = 1000 kgf)
Pound-force (lbf): 4.4482216152605 N (exact, = 0.45359237 kg × 9.80665 m/s²)
Ounce-force (ozf): 0.27801385095378125 N (exact, = lbf / 16; the 16 is a power of 2, so this divison is bit-exact in IEEE-754)
Short ton-force (US, tonf): 8896.443230521 N (exact, = 2000 × lbf)

For the newton → pound-force direction the calculator displays the irrational quotient 1/4.4482216152605 = 0.22480894309971… lbf/N. Most casual converters print 0.2248 and stop there; this one will print as many digits as the precision selector requests, up to 15. The same applies to the kilonewton → pound-force ratio: 1000 / 4.4482216152605 = 224.808943099710… lbf/kN (the classic aerospace thrust conversion). Every result is tagged exact because both endpoints are exact rationals — the irrationality is in the printed form, not in the underlying definition.

Worked Force Conversion Examples

1000 lbf to newtons (aerospace and structural-load workhorse)

Set From = Pound-force, To = Newton, Value = 1000. The formula gives 1000 × 4.4482216152605 = 4448.2216152605 N exact. At auto-precision the result reads 4448.22 N (6 significant figures). Set precision to 15 decimals to see the full mantissa. This is the conversion every US-trained aerospace or structural engineer does daily when reading a metric specification: a 1,000-lbf payload attachment maps to 4.45 kN of design load, and the 0.000486% gap between the casual 4.4482 rounding and the exact 4.4482216152605 figure drifts by ~0.0216 N over 1000 lbf — invisible for a single bracket, and still only ~21.6 N (~4.86 lbf) over a 1,000,000-lbf rocket-stage load budget, but it grows large enough to matter at primary-force-standard metrology scales.

1 kgf to newtons (every motor catalogue and hydraulic spec)

Set From = Kilogram-force, To = Newton, Value = 1. The formula gives 1 × 9.80665 = 9.80665 N exact. This is the single cleanest gravitational-to-SI conversion in the whole table because the CGPM-1901 declaration fixes standard gravity at exactly 9.80665 m/s², no rounding involved. Hydraulic-cylinder catalogues, electric-motor torque ratings (in kgf·m), and elevator load specifications still quote kgf in many European and Asian markets; the SI equivalent is what every modern finite-element-analysis (FEA) package expects. A 1000 kgf hydraulic ram = 9806.65 N exact (= 1 tnf, the tonne-force).

Saturn V F-1 engine thrust: 1,522,000 lbf to MN (historical anchor)

Set From = Pound-force, To = Newton, Value = 1522000. The formula gives 1,522,000 × 4.4482216152605 = 6,770,193.298 N exact, or 6.77 MN — the often-quoted thrust of the upgraded Rocketdyne F-1 engine used on Apollo 8 and beyond. Each Saturn V first stage carried five F-1 engines, giving a total liftoff thrust of 5 × 6.77 MN ≈ 33.85 MN (the canonical “7.6 million pounds of thrust” figure NASA quotes is the original 1,500,000-lbf rating × 5 = 7.5 × 10⁶ lbf ≈ 33.4 MN). The Saturn V is a closed historical programme — these numbers do not decay with time and make a useful sanity benchmark for any newer thrust comparison.

70 kgf to newtons (the bathroom-scale conversion)

Set From = Kilogram-force, To = Newton, Value = 70. The formula gives 70 × 9.80665 = 686.4655 N exact. This is what your bathroom scale actually measures when it shows “70 kg”. Strictly speaking, a bathroom scale reads force (the weight you exert on the spring or strain gauge) and divides by local gravitational acceleration to display a number labelled “kg”. Because most consumer scales are calibrated for a single nominal g (typically 9.80665), the displayed “kg” is really the kgf — and the underlying physical quantity is 686.5 N of force, not 70 kg of mass. On the Moon, a scale calibrated for Earth would still show 70 “kg” only if it knew the local g; an uncalibrated spring scale would show about 11.6 kgf because lunar g is ~1.625 m/s².

1 dyne to newtons (the physics-textbook unit conversion)

Set From = Dyne, To = Newton, Value = 1. The formula gives 1 × 1e-5 = 1e-5 N exact, equivalently 10 µN (micronewtons). This is the canonical CGS-to-SI conversion every introductory physics course tests. The dyne survives in three modern niches: surface tension (water at 25 °C: ~72 dyn/cm = 72 mN/m), small-scale biomechanics (cardiac contractility), and historical electromagnetism literature (gauss × abampere = dyne / abcoulomb). In every modern engineering spec, the equivalent SI value in millinewtons or micronewtons is preferred — 1 dyne = 10 µN is the cleanest mnemonic.

Comparative table: 1 unit in newtons and pound-force

Unit	Value in N	Value in lbf	Value in kgf	Exact?
Dyne (dyn)	1 × 10⁻⁵	2.2481 × 10⁻⁶	1.01972 × 10⁻⁶	yes
Ounce-force (ozf)	0.27801385095378125	0.0625 (= 1/16)	0.028349523125	yes
Newton (N)	1	0.22480894309971	0.101971621298	yes
Pound-force (lbf)	4.4482216152605	1	0.45359237	yes
Kilogram-force (kgf)	9.80665	2.20462262184878	1	yes
Kilonewton (kN)	1000	224.808943099710	101.971621297793	yes
Short ton-force (US tonf)	8896.443230521	2000	907.18474	yes
Tonne-force (tnf)	9806.65	2204.62262184878	1000	yes

Three definitional shortcuts worth memorising: 1 lbf = 0.45359237 kgf exact (the IYP-1959 pound expressed as kgf, with g_n cancelling); 1 kgf = 9.80665 N exact (the CGPM-1901 anchor); 1 short ton-force = 2000 lbf exact = ~907.18 kgf (about 91% of a tonne-force). All other rows are exact rationals that follow from these definitions and the SI newton.

Force Conversion Tips

Treat 1 lbf ≈ 4.45 N as a back-of-envelope approximation only. The exact relationship is 1 lbf = 4.4482216152605 N, fixed by the 1959 International Yard and Pound Agreement (1 lb = 0.45359237 kg exact) and the 3rd CGPM 1901 declaration (g_n = 9.80665 m/s² exact). For mental conversions “multiply by 4.5” gets you within 1.2% (drift of ~5 N per 100 lbf). For datasheet, CAD or finite-element work, work in newtons first and convert to lbf only at the last step using the full 4.4482216152605 factor.
Memorise the four exact pivots through the newton: kilonewton (1000), pound-force (4.4482216152605), kilogram-force (9.80665) and dyne (1e-5). Every conversion in this tool is implemented as “input × from-factor ÷ to-factor”, so memorising these four gives you the entire cross-table in your head. Ounce-force (lbf / 16), tonne-force (1000 × kgf) and short ton-force (2000 × lbf) round out the set.
kgf is not kg. On the bathroom scale, the number reading “70 kg” is actually a force measurement of about 686.5 N, displayed as 70 kgf using the convention 1 kgf = 9.80665 N exact. Mass is intrinsic and doesn’t change with gravity; force depends on g. The scale displays mass-as-if only because consumer scales are calibrated for one nominal g. In engineering specs, never write “100 kg of load” when you mean “100 kgf” — it confuses mass and force at the design-review level.
lbf is not lbm (and neither is a slug). In US engineering, pound-force (lbf) is force, pound-mass (lbm) is mass, and the slug is the FPS mass unit defined as the mass that 1 lbf accelerates at 1 ft/s² (so 1 slug = 32.174 lbm). The historical confusion is that 1 lbm weighs exactly 1 lbf under standard gravity on Earth, which makes the two numerically identical there — but they collapse only at sea-level Earth gravity. In any dynamic problem (F = m·a), use slugs for mass if you stay in lbf, or convert to SI and use kg + N.
Use the precision selector to match your audience. Casual conversions round to 0–2 decimals (a 100-lbf payload is just “445 N” in a hallway conversation). Engineering datasheets quote 4–6 decimals. Aerospace thrust audits and structural FEA inputs typically work to 6–10 decimals because cumulative error over a million-Newton thrust budget can shift performance margins. Metrologists comparing against a primary force standard want 15 decimals — the full IEEE-754 double mantissa exposed by this calculator.
Every force unit in this set is exact. Unlike length conversions involving the light-year or parsec, where IAU definitions exceed 64-bit double precision, every force factor here is a finite rational that fits cleanly in IEEE-754: 1, 1000, 1e-5, 9.80665, 9806.65, 4.4482216152605, 0.27801385095378125 (= lbf/16, a power-of-2 division that preserves bit-exactness), 8896.443230521 (= 2000 lbf). The “exact” badge fires for every pair.
Tonne-force (≈ 9.81 kN) is not the same as short ton-force (≈ 8.90 kN). 1 tonne-force = 1000 kgf = 9806.65 N exact (based on 1000 kg of mass under standard gravity). 1 short ton-force = 2000 lbf = 8896.443230521 N exact (based on 2000 avoirdupois pounds, ~907.185 kg). The two differ by ~9.3% — a non-trivial gap on any heavy-equipment specification, cargo crane rating or press tonnage. Always disambiguate with the explicit “tonne-force (metric)” or “short ton-force (US)” label, never just “ton”.
When the result is larger than 10¹² (one trillion) or smaller than 10⁻³ at auto-precision, the display switches to scientific notation. This is on purpose: writing the Saturn V first-stage thrust (~34 MN) in dynes as 3,400,000,000,000 dyn is unreadable, while 3.4e12 dyn is parseable at a glance.
For aerospace thrust ratings, expect specs in lbf (US-trained programmes), kN (modern European, Indian, Chinese, Japanese launchers) or MN (very large stages). 1 MN = 224,809 lbf exact (well, exact up to the 0.2248… irrational quotient); the Saturn V F-1 engine’s 6.77 MN ≈ 1.522 × 10⁶ lbf is a useful historical anchor that doesn’t decay with time. For drone and model-rocket motors, expect grams-force (gf, where 1 gf = 9.80665 mN) or ounces-force (1 ozf = 0.27801385 N), both flagged exact in this calculator.

Force Converter — Frequently Asked Questions

Is this force converter free?

Yes. The calculator is free, requires no account, runs entirely in your browser, and is ad-free. The embeddable iframe version at /en-US/widget/force-converter is also free and ad-free, so you can drop it into engineering portals, aerospace blogs, physics-education pages or hydraulic-equipment catalogues without exposing readers to third-party trackers.

How accurate are the force conversion factors?

Every factor in this converter is exact. The newton and kilonewton are exact by SI definition. The dyne is exact by CGS definition (1 dyn = 1e-5 N). The gravitational units (kgf, tonne-force, lbf, ozf, short ton-force) are exact because two upstream definitions are exact: the 1959 International Yard and Pound Agreement (1 lb = 0.45359237 kg) and the 3rd CGPM 1901 declaration (g_n = 9.80665 m/s²). 1 lbf = 0.45359237 × 9.80665 = 4.4482216152605 N has zero rounding error — any “4.4482” you see in a textbook is a 4-decimal truncation.

How many newtons are in a pound-force?

Exactly 4.4482216152605 newtons. The number is not measured; it is defined, as 0.45359237 kg (the 1959 international avoirdupois pound) times 9.80665 m/s² (the CGPM 1901 standard gravity). Most casual references quote 4.4482 N or 4.448 N, which are five- and four-significant-figure roundings. For surveying, aerospace and metrology work, use the full 13-digit value or the 15-digit IEEE-754 representation.

What is the difference between kg and kgf?

Kilogram (kg) is the SI unit of mass — an intrinsic property of matter that does not change with gravity. Kilogram-force (kgf) is a non-SI unit of force, equal to exactly 9.80665 N. A 70 kg person has a mass of 70 kg everywhere in the universe, but a weight of about 70 kgf only on Earth at standard gravity; on the Moon their weight is about 11.6 kgf. Bathroom scales display “kg” but actually measure force in kgf, dividing internally by g_n.

Is 1 kgf the same as 1 kg?

No. Kg is mass; kgf is force. They are numerically equal only on Earth at standard gravity (9.80665 m/s²), where a 1-kg object has a weight of exactly 9.80665 N = 1 kgf. Mass stays constant in space; weight in kgf changes with local g.

What is the difference between lbf, lbm and a slug?

All three exist in US engineering, and the confusion is real. Pound-force (lbf) is force, equal to exactly 4.4482216152605 N. Pound-mass (lbm) is mass, equal to exactly 0.45359237 kg by the 1959 IYP agreement. A slug is the FPS mass unit defined as the mass that 1 lbf accelerates at 1 ft/s² — so 1 slug = 32.174 lbm (the numerical value of standard gravity in ft/s²). They collapse to numerical equality only at Earth’s surface: a 1-lbm object weighs 1 lbf under standard gravity. In any dynamic problem, use slugs with lbf, or convert to kg + N.

Why is g_n exactly 9.80665 m/s²?

Because the 3rd General Conference on Weights and Measures (CGPM) in 1901 declared it so. The value is not the measured gravitational acceleration at any particular spot on Earth (the real number ranges from ~9.78 m/s² at the sea-level equator to ~9.834 m/s² near the poles, dipping as low as ~9.764 m/s² atop Mt. Chimborazo); it is an exact conventional constant adopted to anchor units like kgf and lbf to the SI newton. Once g_n is exact, the kgf factor (9.80665 N), the lbf factor (0.45359237 × 9.80665 = 4.4482216152605 N), and all the ton-force factors become exact rationals.

How many newtons in 1 kN?

Exactly 1000 newtons. The prefix “kilo” is a definitional SI multiplier of 10³. Kilonewtons dominate modern engineering specifications: a typical car’s braking force is around 7–12 kN, a fully-loaded passenger lift cable carries ~30–60 kN, and a single Falcon 9 Merlin engine produces ~845 kN at sea level.

What is a tonne-force and how is it different from a metric ton?

A tonne (metric ton) is a unit of mass equal to 1000 kg exactly. A tonne-force (tnf) is a unit of force equal to 1000 kgf = 9806.65 N exactly — the weight of 1000 kg under standard gravity. A 5-tonne press exerts about 5 tnf = 49,033 N = 11,023 lbf of force when loaded to capacity. The two are commonly conflated in industrial catalogues because they’re numerically the same on Earth, but the physical quantity matters when the spec moves to aerospace, orbital or extraterrestrial contexts.

Why does 1 newton in lbf give an irrational decimal?

Because the exact definition runs the other way: 1 lbf is exactly 4.4482216152605 N. The inverse 1/4.4482216152605 = 0.22480894309971… lbf/N is mathematically irrational — there is no last digit, only a longer truncation. Engineering tables almost always print 0.2248 or 0.22481; this calculator will show whatever precision you ask for, up to 15 decimal digits.

How much thrust did a Saturn V F-1 engine produce in newtons?

About 6.77 MN per engine on the upgraded post-Apollo-8 version, or about 6.67 MN on the original 1,500,000-lbf rating. The exact arithmetic: 1,522,000 lbf × 4.4482216152605 N/lbf = 6,770,193.298 N. The Saturn V first stage carried five F-1 engines, so total liftoff thrust was roughly 5 × 6.77 MN ≈ 33.85 MN (the canonical “7.6 million pounds of thrust” in NASA materials is the slightly lower 1,500,000-lbf rating across all five). These are historical anchors; the programme ended in 1973.

Can I embed this force converter on my site?

Yes. The embeddable version lives at /en-US/widget/force-converter; copy the iframe snippet from the embed page. The iframe is ad-free, dependency-free, mobile-responsive, and inherits no third-party trackers — useful for engineering portals, aerospace and physics blogs, hydraulic and mechanical-equipment catalogues, and STEM-education pages that need a converter without ad noise.

Key Force Conversion Terms

Newton (N)

The SI derived unit of force, defined as 1 N ≡ 1 kg⋅m/s² — the force required to accelerate a 1-kg mass at 1 m/s². Named after Isaac Newton and adopted as the SI unit of force at the 9th CGPM in 1948. Standard for all modern scientific publishing, engineering specifications outside the US, and physics education. Wikidata: Q12438.

Kilonewton (kN)

An SI unit of force equal to exactly 1000 N. The dominant unit in structural engineering, aerospace thrust ratings (post-1980 European, Indian, Chinese, Japanese launchers) and heavy-equipment specifications. A typical passenger car’s peak braking force is ~7–12 kN; a Boeing 737 engine’s thrust is ~120 kN per engine.

Pound-force (lbf)

A US customary and imperial unit of force, equal to exactly 4.4482216152605 N. Defined as the force exerted on one avoirdupois pound (0.45359237 kg exact, IYP 1959) under standard gravity (9.80665 m/s² exact, CGPM 1901). The dominant unit in US-trained aerospace, structural and mechanical engineering. Distinct from pound-mass (lbm) and from the slug. Wikidata: Q1194225.

Kilogram-force (kgf, kp)

A non-SI unit of force equal to exactly 9.80665 N — the weight of one kilogram of mass under standard gravity. Also called the kilopond (kp). Listed by BIPM as deprecated but still common in European and Asian hydraulic, motor-torque and elevator-load specifications. The number on a bathroom scale labelled “kg” is really a kgf reading. Wikidata: Q216880.

Dyne (dyn)

The CGS unit of force, defined as 1 dyn ≡ 1 g⋅cm/s² = exactly 1 × 10⁻⁵ N (10 μN). Proposed by the British Association for the Advancement of Science in 1873. Survives in surface-tension measurements (water at 25 °C: ~72 dyn/cm), small-scale biomechanics and historical electromagnetism literature. Wikidata: Q201933.

Tonne-force (tnf, tf)

A non-SI unit of force equal to exactly 1000 kgf = 9806.65 N. The weight of one metric tonne (1000 kg) under standard gravity. Common in heavy-industrial catalogues (press tonnage, crane ratings) in metric countries. Distinct from the short ton-force (US, ~8896 N) and long ton-force (UK, ~9964 N).

Short ton-force (tonf, US)

A US customary unit of force equal to exactly 2000 lbf = 8896.443230521 N. The weight of one short ton (2000 lb, ~907.185 kg) under standard gravity. About 9.3% smaller than a tonne-force. Standard in US heavy-press, crane and shipping-capacity specifications.

Ounce-force (ozf)

A US customary unit of force equal to exactly 1/16 of a pound-force = 0.27801385095378125 N. Because the divisor 16 is a power of 2, the conversion is bit-exact in IEEE-754 double-precision arithmetic. Used in small-component testing (precision torque, instrument-spring tension) and model-aircraft motor thrust ratings.

Standard gravity (g_n)

The conventional gravitational acceleration on Earth’s surface, fixed at exactly 9.80665 m/s² by the 3rd CGPM in 1901. Not a measured value at any particular point (real values range from 9.764 to 9.834 m/s² over the Earth’s surface), but an exact defined constant that anchors every gravitational force unit (kgf, lbf, ton-force) to the SI newton. Wikidata: Q13400897.

Pound-mass (lbm)

A US customary unit of mass equal to exactly 0.45359237 kg, fixed by the 1959 International Yard and Pound Agreement. Distinct from pound-force (lbf): 1 lbm has a weight of 1 lbf only at Earth’s standard gravity. In any dynamics problem (F = m·a), use the slug as the mass unit if you stay in lbf — 1 slug = 32.174 lbm. Conflating lbm and lbf is the single most common source of unit errors in US engineering coursework.

Slug

The FPS (foot-pound-second) unit of mass, defined as the mass that 1 pound-force accelerates at 1 ft/s². Equal to exactly 14.59390294 kg ≈ 32.174 lbm. Less commonly used than lbm in everyday US engineering, but mathematically essential for any F = m·a calculation that stays in customary units; the alternative is the awkward “gravitational conversion factor” g_c = 32.174 lbm·ft/(lbf·s²).

Exact factor

A conversion factor fixed by international definition or international agreement, with zero rounding error. For force, every factor in this calculator is exact: 1 kN = 1000 N, 1 dyn = 1e-5 N, 1 kgf = 9.80665 N, 1 lbf = 4.4482216152605 N, 1 ozf = lbf/16, 1 tonf = 2000 lbf. NIST SP 811 Appendix B.8 prints exact factors in boldface.

International Yard and Pound Agreement (1959)

Multilateral agreement signed by the US, UK, Canada, Australia, New Zealand and South Africa, effective 1 July 1959. It defined the avoirdupois pound as exactly 0.45359237 kg, which combined with standard gravity gives the exact pound-force factor of 4.4482216152605 N.

3rd CGPM (1901)

The 3rd General Conference on Weights and Measures, held in Paris in 1901, which declared standard gravity g_n = 9.80665 m/s² as an exact defined constant. This single declaration is what makes every gravitational force unit (kgf, tonne-force, lbf, ozf, ton-force) reducible to an exact factor in newtons.

Significant figures

The digits in a numerical result that carry meaning about its precision. Auto-precision in this calculator targets 6 significant figures, the default for engineering tables. NIST SP 811 force factors are typically quoted to 7–9 significant figures so that any rational rounding of an exact factor is unambiguous.

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