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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.

lbf

Result

4.44822 N

1 lbf= 4.448222 N

UnitValue
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
Volume ConverterTorque Converter

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?

Is a "kilogram of force" the same thing as a kilogram of mass? Not quite — and that gap is the reason force units are so confusing. The same everyday words, "kilo" and "pound", each name two different physical quantities: an amount of matter (mass) and a push or pull (force). What bridges them is gravity. A 1 kg mass sitting on Earth presses down with a force, and at standard gravity (g = 9.80665 m/s²) that force is exactly 9.80665 newtons — which is precisely how the kilogram-force (kgf) is defined. The pound works the same way: a 1-pound mass weighs about 4.448 newtons, and that weight is the pound-force (lbf). So kgf and lbf exist purely because people wanted to talk about "the weight of a kilo" or "the weight of a pound" without doing the gravity multiplication every time. The catch worth remembering: that mass-to-force equivalence only holds at standard gravity. Carry the same 70 kg mass to the Moon and its mass is still 70 kg, but its weight drops to about 11.6 kgf because lunar gravity is roughly one-sixth of Earth's.
This converter resolves all of that by routing every unit through one base — the newton (N), the SI unit of force — 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. gn = 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 gn 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⋅afromatoy = x \cdot \frac{a_{\text{from}}}{a_{\text{to}}}
where x is your input value, afrom is the source unit's factor to newtons, and ato is the target unit's factor to newtons. To do it by hand:
1. Look up the source-to-newton factor. For pound-force, afrom = 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, ato = 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 × gn with gn 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.

Common Force Conversions at a Glance

FromToValueExact?
1 NewtonPound-force0.224809 lbfyes
1 NewtonKilogram-force0.101972 kgfyes
1 Pound-forceNewton4.4482216152605 Nyes
1 Kilogram-forceNewton9.80665 Nyes
1 KilonewtonKilogram-force101.972 kgfyes
1 KilonewtonPound-force224.809 lbfyes
1 Pound-forceKilogram-force0.45359237 kgfyes
1 DyneNewton0.00001 N (10 µN)yes
1 NewtonDyne100000 dynyes
1 Tonne-forceKilonewton9.80665 kNyes
1 Short ton-forceKilonewton8.896443 kNyes

Force Conversion Formula

y=x⋅afromatoy = x \cdot \frac{a_{\text{from}}}{a_{\text{to}}}
  • yy = The converted value, expressed in the target unit of force.
  • xx = The input value, expressed in the source unit of force.
  • afroma_{\text{from}} = Factor that converts the source unit to newtons (e.g. 9.80665 for kgf, 4.4482216152605 for lbf, 1e-5 for dyne).
  • atoa_{\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 gn = 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

UnitValue in NValue in lbfValue in kgfExact?
Dyne (dyn)1 × 10⁻⁵2.2481 × 10⁻⁶1.01972 × 10⁻⁶yes
Ounce-force (ozf)0.278013850953781250.0625 (= 1/16)0.028349523125yes
Newton (N)10.224808943099710.101971621298yes
Pound-force (lbf)4.448221615260510.45359237yes
Kilogram-force (kgf)9.806652.204622621848781yes
Kilonewton (kN)1000224.808943099710101.971621297793yes
Short ton-force (US tonf)8896.4432305212000907.18474yes
Tonne-force (tnf)9806.652204.622621848781000yes
Three definitional shortcuts worth memorising: 1 lbf = 0.45359237 kgf exact (the IYP-1959 pound expressed as kgf, with gn 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 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 (gn = 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 gn.

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 gn 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.

Sources & References

  1. NIST SP 811 Appendix B.8 — Factors for units listed alphabetically (exact force factors in boldface: pound-force 4.4482216152605 N, kilogram-force 9.80665 N, dyne 1e-5 N, all definitionally exact)
  2. NIST Guide to the SI, Appendix B — Conversion factors (landing page, with the canonical bold-is-exact convention)
  3. BIPM — Resolution of the 3rd CGPM (1901): declaration that standard gravity g_n = 9.80665 m/s² exact, the upstream constant that makes every gravitational force unit (kgf, tonne-force, lbf, ozf, ton-force) reducible to an exact newton factor
  4. BIPM — The International System of Units (SI Brochure, 9th edition 2019): the newton (1 N ≡ 1 kg·m/s²) is the SI derived unit of force; the kilogram-force and other gravitational units are not accepted for use with the SI
  5. Wikipedia — Newton (unit): the SI derived unit of force, 1 N = 1 kg·m/s², adopted at the 9th CGPM in 1948 (Wikidata Q12438)
  6. Wikipedia — Pound (force): defined as exactly 0.45359237 kg × 9.80665 m/s² = 4.4482216152605 N; covers the lbf vs lbm vs slug distinction (Wikidata Q1194225)
  7. Wikipedia — Kilogram-force: weight of one kilogram of mass under standard gravity, equal to exactly 9.80665 N; deprecated by BIPM but still common in hydraulic and motor catalogues (Wikidata Q216880)
  8. Wikipedia — Dyne: the CGS unit of force, equal to exactly 1 × 10⁻⁵ N (10 μN); survives in surface-tension measurements, biomechanics and historical electromagnetism (Wikidata Q201933)
  9. Wikipedia — Standard gravity: g_n = 9.80665 m/s² is an exact conventional constant fixed by the 3rd CGPM (1901), not a measured value at any specific point on Earth (Wikidata Q13400897)
  10. Wikipedia — International Yard and Pound Agreement (1 July 1959): defined the avoirdupois pound as exactly 0.45359237 kg, the upstream constant for pound-force, ounce-force and short ton-force

Content verified by the Smart Calculators Team