Newton — the SI standard
The newton is defined absolutely: 1 N = 1 kg·m/s². It's gravity-independent — a 1 N force is the same on Earth, Mars, or in deep space. All modern physics and most engineering use the newton.
Force Converter
Free June 6, 2026
Need to convert 1500 N to lbf for a torque wrench spec? Convert kip to kN for a structural drawing? Or work out how many dynes are in a kilogram-force for a physics problem? This free force converter handles all 15 common force units — SI, metric, US/imperial, and ton variants — with the exact conversion factors used by NIST and BIPM. Type a value, pick a unit, and get the answer in every other unit at once.
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What is force?
Force is what makes things accelerate, stretch, compress, bend, or change direction. Isaac Newton wrote it down as F = ma — force equals mass times acceleration. Push a 1 kg object so it speeds up at 1 m/s², and you've applied exactly 1 newton. The newton (N) is the SI base unit, but engineers, physicists, and US tradespeople use many other units for historical reasons — pound-force, kilogram-force, kip, dyne, poundal, and several ton variants. They all measure the same physical quantity; only the scale and definitions differ. This converter handles all 15 common units with exact conversion factors.
Four things to know about force units
Force units come in two flavors — gravitational (defined by what 'X kilograms weighs') and absolute (defined by F = ma). Mixing them up is the #1 source of conversion errors.
kgf and lbf — gravity-based
Kilogram-force and pound-force are defined as the weight of 1 kg (or 1 lb) under standard Earth gravity. They embed g = 9.80665 m/s² in the unit, which is why 1 kgf = 9.80665 N. Convenient when working with mass, but technically obsolete in SI.
kip and kN — the engineering scale
Structural engineers don't think in single newtons or pounds — they think in thousands. 1 kip = 1000 lbf and 1 kN = 1000 N. A typical floor live load is around 50 lbf/ft² (≈ 2.4 kN/m²), and a steel I-beam might support 50 kips (≈ 222 kN).
dyne and poundal — historical CGS units
The dyne (CGS metric) and poundal (CGS imperial) are absolute units like the newton, but tiny: 1 N = 100,000 dynes = 7.23 poundals. They survive in old physics textbooks and in surface tension (dyn/cm). Almost never used in modern engineering.
Common force values in everyday units
A practical reference for the magnitudes you'll actually encounter — from the weight of a paperclip to the thrust of a Saturn V. Compare units side by side to build intuition.
| Object / Source | Newtons (N) | Pound-force (lbf) | kgf |
|---|---|---|---|
| Weight of a paperclip (~1 g) | 0.0098 N | 0.0022 lbf | 0.001 kgf |
| Weight of a smartphone (~200 g) | 1.96 N | 0.44 lbf | 0.2 kgf |
| Weight of an apple (~150 g) | 1.47 N | 0.33 lbf | 0.15 kgf |
| Weight of a 1 kg bag of flour | 9.81 N | 2.20 lbf | 1 kgf |
| Weight of an adult (~70 kg) | 686.5 N | 154.3 lbf | 70 kgf |
| Bite force, human jaw (max) | 720 N | 162 lbf | 73 kgf |
| Weight of a small car (~1500 kg) | 14,710 N | 3,307 lbf | 1,500 kgf |
| Tow truck pulling force (typical) | 20,000 N | 4,496 lbf | 2,039 kgf |
| Boeing 747 thrust per engine | 281,600 N | 63,300 lbf | 28,716 kgf |
| Saturn V rocket thrust (total) | 35,100,000 N | 7,891,000 lbf | 3,579,000 kgf |
Values shown use standard gravity (g = 9.80665 m/s²) for kgf calculations. Real-world g varies ~0.5% between equator and poles, but the difference rarely matters for engineering work.
The math behind force conversion
Force conversion is just multiplication by a fixed factor — but understanding where the factors come from helps you spot errors. Here are the four formulas you actually need.
Newton's second law (definition of force)
F = m × a
Force equals mass times acceleration. With m in kilograms and a in m/s², F comes out in newtons. This is the definition the newton is built on — everything else converts to or from this.
A 5 kg object accelerating at 2 m/s² experiences F = 5 × 2 = 10 N.
Weight from mass (gravitational force)
W = m × g
Weight is the gravitational force on a mass. On Earth, g = 9.80665 m/s² (the 'standard gravity' fixed by international agreement). So a 1 kg mass weighs 9.80665 N — which is exactly what 1 kgf is defined as.
An 80 kg person weighs W = 80 × 9.80665 = 784.5 N (= 80 kgf = 176.4 lbf).
Convert between any two force units
F_target = F_source × (factor_source / factor_target)
Where 'factor' is each unit's conversion-to-newtons factor. The two factors form a ratio, so the source unit cancels and you're left with the target. This is how every conversion in the table above is computed.
Convert 100 lbf to N: 100 × (4.4482 / 1) = 444.82 N. Convert 500 N to kgf: 500 × (1 / 9.80665) = 50.99 kgf.
Pound-force from pound-mass × standard g
1 lbf = 1 lb × g₀ = 0.45359237 kg × 9.80665 m/s² ≈ 4.4482 N
This is where the 'messy' lbf-to-N factor comes from. The avoirdupois pound (0.45359237 kg) was fixed exactly in 1959; standard gravity (9.80665 m/s²) was fixed exactly in 1901. Their product is exact: 4.4482216152605 N per lbf — just not a round number.
1 lbf to N = 0.45359237 × 9.80665 = 4.44822... — verify with the calculator above.
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Mass vs Force vs Weight — three things people mix up
If you remember just one thing about force units: kilograms measure MASS, newtons measure FORCE, and 'weight' is a force, not a mass. Most conversion errors come from forgetting which is which.
Mass (kilogram, kg)
How much matter an object contains. A 70 kg person has 70 kg of mass on Earth, on the Moon, on Mars, or in space — mass doesn't change with location.
- SI unit: kilogram (kg)
- Imperial unit: pound-mass (lb or lbm)
- Measured by an inertial scale (or balance against a known mass)
- Stays constant everywhere in the universe
Force / Weight (newton, N or kgf or lbf)
How hard something pushes or pulls. Weight is the specific force that gravity exerts on a mass. A 70 kg person weighs 686.5 N on Earth, but only 113.7 N on the Moon (g_moon ≈ 1.62 m/s²).
- SI unit: newton (N)
- Imperial units: lbf, kip, poundal
- Measured by a spring scale or strain gauge
- Changes with gravity (kgf and lbf assume Earth's standard g)
| Quantity | Earth (g = 9.81 m/s²) | Moon (g = 1.62 m/s²) | ISS in orbit (g_eff ≈ 0) |
|---|---|---|---|
| Mass of a 70 kg person | 70 kg | 70 kg | 70 kg |
| Weight (in N) | 686.5 N | 113.7 N | ≈ 0 N |
| Weight (in lbf) | 154.3 lbf | 25.5 lbf | ≈ 0 lbf |
| Weight (in kgf) | 70 kgf | 11.6 kgf | ≈ 0 kgf |
Mass is conserved; weight depends on where you are. This is why 'kg' and 'kgf' are not the same — and why a torque spec in kgf·m means something different on the Moon (if you brought your wrench).
Quick force conversions you can do in your head
Don't always need full precision. These rules of thumb get you within 1-2% — fine for back-of-the-envelope checks before pulling up the calculator. Memorize the first three and you'll handle 90% of cases.
| From | To | Rule of thumb | Exact factor |
|---|---|---|---|
| kgf | N | Multiply by 10 (then subtract ~2%) | × 9.80665 |
| N | kgf | Divide by 10 (then add ~2%) | ÷ 9.80665 |
| lbf | N | Multiply by 4.5 | × 4.4482 |
| N | lbf | Divide by 4.5 | ÷ 4.4482 |
| kN | kip | Divide by 4.5 (same factor as N→lbf) | ÷ 4.4482 |
| kip | kN | Multiply by 4.5 | × 4.4482 |
| lbf | kgf | Divide by 2.2 (lb → kg ratio) | × 0.4536 |
| dyne | N | Move decimal 5 places left | × 0.00001 |
| tf | kN | Multiply by ~10 (close to 9.81) | × 9.80665 |
The fact that lbf→N (× 4.45) and lb→kg (÷ 2.2) share so much DNA isn't coincidence — they both come from the same 1959 international pound definition. Once you internalize 'pound ≈ 0.45 kg' and 'kgf ≈ 10 N,' the rest follows.
Why kgf isn't really a 'unit of mass'
Despite the 'kilogram' in the name, kgf is a unit of FORCE, not mass. This catches people off guard, especially in engineering specs that mix kgf and kg in the same drawing.
Gravitational units (kgf, lbf)
Defined as 'the weight of X mass under standard Earth gravity.' They built g₀ = 9.80665 m/s² into the definition.
- 1 kgf = 9.80665 N (always — by definition)
- 1 lbf = 4.4482 N (always — by definition)
- Convenient: 'a 70 kg person weighs 70 kgf'
- Trap: assumes you're on Earth; meaningless in space
Absolute units (N, dyne, poundal)
Defined from F = ma with no gravity baked in. Truly universal — same on Earth, Mars, ISS, or interstellar space.
- 1 N = 1 kg·m/s² (gravity-independent)
- 1 dyne = 1 g·cm/s² = 10⁻⁵ N
- 1 poundal = 1 lb·ft/s² ≈ 0.138 N
- Required for any physics or aerospace work
| Scenario | kgf description | newton description |
|---|---|---|
| A bolt tightened to '100 kgf·m' on Earth | Works fine — measured on a torque wrench calibrated for Earth | = 980.7 N·m anywhere in the universe |
| The same bolt on the Moon | A '100 kgf·m' torque wrench would only deliver ~16 kgf·m of real torque (gravity is 1/6) | Still 980.7 N·m if you apply that much actual force |
| Atomic-scale force (1 nN) | ≈ 0.0000001 kgf — awkward and meaningless at this scale | 1 nN, clean and dimensionally correct |
When in doubt, use newtons. They're the only force unit guaranteed to behave correctly across every field of physics and every location in the universe.
Same astronaut, different weight
Two physical setups, identical mass, vastly different force readings. Use this to build intuition for what kgf and lbf actually mean — and why they can be misleading away from Earth.
Earth surface (Sarah, 65 kg astronaut)
Standard gravity: g = 9.80665 m/s²
Mass 65 kg
Weight in newtons 65 × 9.80665 = 637.4 N
Weight in kgf 65 kgf
Weight in lbf 143.3 lbf
What a bathroom scale shows
65 kg (it's calibrated for g=9.80665)
Moon surface (same Sarah, same suit)
Lunar gravity: g = 1.625 m/s² (~1/6 of Earth)
Mass 65 kg (unchanged)
Weight in newtons 65 × 1.625 = 105.6 N
Weight in kgf 10.77 kgf (uses Earth's g)
Weight in lbf 23.7 lbf
What a bathroom scale shows
10.77 kg (the scale is fooled — it thinks Sarah's mass shrank)
The mass is identical. The newtons differ by exactly the ratio of gravities (9.80665 / 1.625 = ~6.03). The 'kgf' reading also drops — because kgf is a force unit, despite the misleading name. And a bathroom scale on the Moon would read 10.77 kg, which is wrong if you interpret it as mass. This is why aerospace engineers, biomechanics researchers, and pharmaceutical companies (where dosing is by mass, not weight) always use newtons for force and kilograms for mass — never kgf.
Real-world force conversions
Force conversion isn't just a physics-class exercise. These are the fields where engineers and tradespeople flip between units constantly.
Structural engineering
US drawings spec loads in kips and psi; SI drawings use kN and MPa. Cross-border projects (US firm + European steel) demand fluent conversion. A 50 kip beam capacity = 222 kN; an HSS column rated 200 kN = 45 kip.
Mechanical engineering & torque
Torque specs come in lbf·ft, N·m, kgf·m, and kgf·cm depending on country and decade. A bolt torqued to 100 lbf·ft = 135.6 N·m = 13.8 kgf·m. Get this wrong and you either strip threads or under-torque a critical fastener.
Physics & lab measurement
Surface tension is still reported in dynes per centimeter in many fields (water = 72 dyn/cm = 0.072 N/m). Cell traction forces in micronewtons or piconewtons. Spring constants in N/m or dyn/cm. Lab instruments often output in CGS — you convert to SI for publication.
Aerospace & propulsion
Rocket engines: F-1 (Saturn V) = 1,500,000 lbf = 6,672 kN. SpaceX Merlin = 845 kN = 190,000 lbf. Modern aerospace publishes in kN universally, but legacy specs and US contractors still use lbf — every spec sheet shows both.
5 tips for working with force units
- 1
Always state the unit explicitly
'500 lb' is ambiguous (mass or force?). Write 'lbf' for force, 'lbm' for mass. In SI, this isn't a problem — kg is always mass, N is always force. Most rework on construction sites traces back to ambiguous unit labels on drawings.
- 2
Use newtons for any physics calculation
F = ma only works cleanly in SI. If you start with lbf and slugs, you can make it work, but every textbook formula is written for newtons and kilograms. Convert into SI, do the math, convert results back if needed.
- 3
Watch for kgf vs kg in torque specs
Older Japanese and European specs (especially pre-1990) use kgf·m for torque. Newer specs use N·m. A bolt spec'd at '10 kgf·m' = 98 N·m, not 10 N·m. Always check the unit on torque wrenches and tightening sequences.
- 4
Standard gravity is exactly 9.80665 m/s²
Not 9.81, not 9.8, not 10. That's the value used to define kgf and lbf. Real local gravity varies between 9.78 (equator) and 9.83 (poles), so calibrated scales account for it — but conversions always use 9.80665 exactly.
- 5
When in doubt, work in SI
Pick newtons, do the math, then convert the final answer to whatever unit the audience wants. Mixing imperial and metric mid-calculation is where most errors hide. NASA lost the Mars Climate Orbiter ($125 M) in 1999 over exactly this.
5 common force-conversion mistakes
- 1
Confusing 'pound' with 'pound-force'
When someone says 'this weighs 50 pounds,' they almost always mean 50 lbf. But in physics class, 'lb' can mean pound-mass (lbm), where 50 lbm experiences 50 lbf of weight on Earth. The numbers are the same, but they're different quantities. Always write lbm or lbf to be safe.
- 2
Using 9.81 instead of 9.80665 in published work
9.81 is fine for rough work but introduces a 0.0066% error in kgf and lbf conversions. For published engineering specs, regulatory documents, and scientific papers, use 9.80665 exactly. Small errors compound when bolts get torqued and structures get loaded.
- 3
Mixing ton-force variants without checking
Three different 'tons' exist: metric (9806.65 N), US short (8896.44 N), UK long (9964.02 N). A 100 'ton' rating could mean three different things depending on the country and industry. US trucking = short tons; UK heritage = long tons; everywhere else metric = tonne.
- 4
Forgetting kgf is a force, not a mass
Engineers used to imperial units often write things like 'load the beam to 5000 kgf' and mean a force. But people new to the unit see 'kg' and assume mass. Always clarify on drawings — 'load = 5000 kgf (49 kN)' is unambiguous.
- 5
Round-tripping with too little precision
Convert 100 lbf → 444.8 N, then back to lbf using 4.45 (rounded factor) → you get 99.96 lbf, not 100. For specs and calculations, keep at least 5 significant figures throughout — round only at the final answer.
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Other things people ask about force units
Is weight measured in kg or N?
Strictly: weight is a force and should be measured in newtons (or lbf, kgf). In everyday English, 'weight' usually refers to mass — 'I weigh 70 kg' technically means 'my mass is 70 kg.' Physicists and engineers distinguish, but bathroom scales sell as 'measuring weight in kg' even though they're approximating mass.
How many newtons is a kilogram?
A kilogram isn't a force, so the question doesn't quite make sense — but the WEIGHT of 1 kg on Earth is 9.80665 N. If you weigh 70 kg, you exert 686.5 N of force on the ground. In space, your mass is still 70 kg, but your weight is 0 N (you're in free fall around the Earth).
What's bigger, 1 N or 1 lbf?
1 lbf is bigger. 1 lbf ≈ 4.45 N, so a pound-force is over four times a newton. Put another way: an apple weighs about 1 N; a small bag of sugar weighs about 1 lbf.
Can I use the calculator to convert torque?
Not directly — torque has units of force × distance (N·m, lbf·ft, kgf·m). But the force part of torque follows the same conversions: convert the force unit, leave the distance unit alone, and you're done. E.g., 100 lbf·ft = (100 × 4.4482) N · (1 ft) = 444.82 N·ft = 444.82 × 0.3048 m = 135.58 N·m.
What unit do scientists use for very small forces?
Pico-newtons (pN = 10⁻¹² N) for molecular and atomic forces. Femto-newtons (fN = 10⁻¹⁵ N) for single-molecule biophysics. The calculator handles down to micronewtons (μN) directly; for smaller, multiply N by 1000 to get mN, by 1,000,000 to get μN, and so on.
Why do US engineering schools still teach lbf?
Because US infrastructure, codes, and contracts are still in imperial units. The 2020 ASCE 7 building code uses psf (lbf/ft²) for loads; US steel comes in inch dimensions; US contractors quote in dollars per kip. Until the country switches (no sign of that), engineering grads need to be fluent in both systems.
Frequently asked questions
How many newtons are in 1 pound-force (lbf)?
1 lbf = 4.4482216152605 N exactly. The factor is exact because both the international avoirdupois pound (0.45359237 kg, fixed by treaty in 1959) and standard gravity (9.80665 m/s², fixed by the General Conference on Weights and Measures in 1901) are defined values. For most practical work, 1 lbf ≈ 4.45 N is plenty of precision.
What's the difference between kgf and N?
1 kgf (kilogram-force) is the force that 1 kg of mass exerts under standard Earth gravity = 9.80665 N exactly. Newton is the SI unit of force, defined as the force needed to accelerate 1 kg at 1 m/s². So kgf depends on gravity (and is technically obsolete in SI), while newton is gravity-independent. Engineers in older textbooks and many torque specs still use kgf — multiply by 9.80665 to get newtons.
What is a kip and when do I use it?
A kip (kilopound-force) equals 1000 lbf = 4448.22 N = 4.448 kN. Structural and civil engineers in the US use kips constantly — typical residential loads are in single-digit kips, steel beam capacities in dozens to hundreds of kips. It's a convenience unit, exactly like 'kilonewton' but in imperial units.
How does dyne relate to newton?
1 dyne = 10⁻⁵ N exactly (= 0.00001 N). The dyne is the CGS (centimeter-gram-second) unit of force, defined as the force needed to accelerate 1 gram at 1 cm/s². You'll see it in older physics textbooks, surface tension measurements (dyn/cm), and some atomic physics. Modern SI uses the newton — multiply dyne by 10⁻⁵ to convert.
Is a ton-force the same as a metric ton?
No — they measure different things. A metric ton is a unit of MASS (1000 kg). A tonne-force is a unit of FORCE (the weight of 1000 kg under standard gravity = 9806.65 N = 9.80665 kN). Three ton-force variants exist: metric tonne-force (9806.65 N), US short ton-force (8896.44 N, from 2000 lbf), and UK long ton-force (9964.02 N, from 2240 lbf). Always check which one a spec means.
What's a poundal and why is it different from pound-force?
1 poundal (pdl) = 0.138255 N. Poundal is the 'absolute' imperial unit — the force needed to accelerate 1 lb of mass at 1 ft/s². Pound-force is the 'gravitational' imperial unit — the weight of 1 lb under standard gravity (32.174 ft/s²). So 1 lbf ≈ 32 poundals. Almost nobody uses poundal today; it survives mostly in older physics textbooks where the author wanted to keep mass and force units truly distinct.
Why is the conversion factor between lbf and N not a round number?
Because the imperial pound and metric kilogram were defined independently. The pound was historically a unit of mass tied to a brass weight in London; the kilogram was tied to a platinum-iridium cylinder in Paris. When the 1959 international agreement fixed 1 lb = 0.45359237 kg, the lbf-to-N conversion (lbf = lb × 9.80665 m/s²) came out to 4.4482216152605 — exact but messy. Same reason 1 mile ≠ a clean number of meters.
Is this force converter free?
Yes, 100% free, no signup, no tracking, no daily limit. All conversions happen in your browser using exact factors from NIST and BIPM. Works on any device, including offline once the page is loaded.
Conversion factors & sources
All conversion factors in this calculator are exact values from the international standards bodies. Standard gravity (g = 9.80665 m/s²) is fixed by the 3rd CGPM (1901). The avoirdupois pound (1 lb = 0.45359237 kg) is fixed by the 1959 international agreement between the US, UK, Canada, Australia, New Zealand, and South Africa. The newton, dyne, and SI prefixes are defined in the SI Brochure. All factors carry enough significant figures that round-trip conversion (N → other → N) preserves precision in IEEE 754 doubles.
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