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Force Conversion Overview
The Force Conversion tool converts mechanical force values between newtons, kilonewtons, meganewtons, kilogram-force, gram-force, pound-force, ounce-force, kips, dynes, poundals, and other supported units. Enter a value in one unit to calculate its equivalent in the other units.
The SI unit of force is the newton, symbol N. Force is a vector quantity, meaning it has both magnitude and direction. A unit converter changes the numerical unit of the magnitude; it does not change the physical direction of the force.
How to Use the Force Converter
Select the force unit you already know.
Enter the force value.
Select the required output unit.
Read the converted result.
Confirm that mass units such as kg or lb have not been mistaken for force units such as kgf or lbf.
Keep extra digits during calculation and round the final result to match the measurement uncertainty.
What Is Force?
Force describes an interaction that can change an object's motion or deform it. For constant mass in elementary mechanics, Newton's second law is written as:
F = m × a
Where:
F = force in newtons
m = mass in kilograms
a = acceleration in meters per second squared
One newton is the force required to give a mass of one kilogram an acceleration of one meter per second squared:
1 N = 1 kg·m/s2
General Force Conversion Formula
Each force unit can be represented by a factor in newtons. To convert from one unit to another:
Target value = Source value × Source factor in N / Target factor in N
For example, one pound-force equals exactly 4.4482216152605 N. Therefore:
100 lbf × 4.4482216152605 N/lbf = 444.82216152605 N
SI Force Units and Prefixes
| Unit | Symbol | Equivalent in Newtons |
|---|---|---|
| Exanewton | EN | 1018 N |
| Petanewton | PN | 1015 N |
| Teranewton | TN | 1012 N |
| Giganewton | GN | 109 N |
| Meganewton | MN | 106 N |
| Kilonewton | kN | 103 N |
| Hectonewton | hN | 102 N |
| Dekanewton | daN | 10 N |
| Newton | N | 1 N |
| Decinewton | dN | 10-1 N |
| Centinewton | cN | 10-2 N |
| Millinewton | mN | 10-3 N |
| Micronewton | µN | 10-6 N |
| Nanonewton | nN | 10-9 N |
| Piconewton | pN | 10-12 N |
| Femtonewton | fN | 10-15 N |
| Attonewton | aN | 10-18 N |
SI symbols are case-sensitive. MN means meganewton, while mN means millinewton. They differ by a factor of one billion.
Common Non-SI Force Units
| Unit | Symbol | Equivalent in Newtons | Definition or Context |
|---|---|---|---|
| Dyne | dyn | 0.00001 N | CGS force unit |
| Gram-force or pond | gf or p | 0.00980665 N | Force of 1 g mass under standard gravity |
| Kilogram-force or kilopond | kgf or kp | 9.80665 N | Force of 1 kg mass under standard gravity |
| Ounce-force | ozf | 0.278013850953781 N | 1/16 pound-force |
| Pound-force | lbf | 4.4482216152605 N | Force of 1 avoirdupois pound mass under standard gravity |
| Kip | kip | 4448.2216152605 N | 1000 lbf |
| Poundal | pdl | 0.138254954376 N | Force accelerating 1 lb mass at 1 ft/s2 |
| Short ton-force | short tonf | 8896.443230521 N | 2000 lbf |
| Long ton-force | long tonf | 9964.01641818352 N | 2240 lbf |
| Sthene | sn | 1000 N | Historical metre-tonne-second force unit |
Correcting the Kip Conversion
One kip is exactly 1000 pound-force. Using the exact pound-force definition:
1 kip = 1000 × 4.4482216152605 = 4448.2216152605 N
The value 4448.3985765125 N shown in the old page is not consistent with the international pound and standard-gravity definitions and has been corrected.
Mass and Force Are Different
| Quantity | Example Unit | What It Describes |
|---|---|---|
| Mass | kg, g, lb | Inertial property or amount of matter |
| Force | N, kgf, lbf | A push, pull, or weight force |
A kilogram is a unit of mass. A kilogram-force is a unit of force. They cannot be treated as the same physical quantity even though the names are similar.
Weight Force and Standard Gravity
The weight force of a mass in a gravitational field is:
W = m × g
Standard gravity is defined as:
gn = 9.80665 m/s2
Therefore, under standard gravity:
1 kg mass has a weight force of 9.80665 N.
1 g mass has a weight force of 0.00980665 N.
1 lb mass has a weight force of 1 lbf.
Local gravitational acceleration varies with latitude, altitude, and location. kgf and lbf use standard gravity by definition; a real object's local weight force may differ slightly.
Newtons, Kilogram-Force, and Pound-Force
| Starting Force | Newtons | Kilogram-Force | Pound-Force |
|---|---|---|---|
| 1 N | 1 N | 0.1019716213 kgf | 0.2248089439 lbf |
| 1 kgf | 9.80665 N | 1 kgf | 2.2046226218 lbf |
| 1 lbf | 4.4482216152605 N | 0.45359237 kgf | 1 lbf |
Dyne and Newton Conversion
The dyne is the CGS unit of force:
1 dyn = 10-5 N
1 N = 100000 dyn
1 kN = 100000000 dyn
Therefore, 1 dyne equals 10-8 kN, which agrees with the original conversion table.
Equivalent Compound SI Expressions
Some compound units have the same physical dimensions as force:
| Expression | Equivalent Force | Comment |
|---|---|---|
| 1 J/m | 1 N | Energy change per unit displacement |
| 1 J/cm | 100 N | One joule divided by 0.01 metre |
| 1 kg·m/s2 | 1 N | SI base-unit expression |
Although J/m is dimensionally equivalent to N, use the unit that best communicates the physical quantity in the application.
Worked Force Conversion Examples
Newtons to Kilogram-Force
Convert 250 N to kilogram-force:
250 / 9.80665 = 25.4929 kgf
Newtons to Pound-Force
Convert 250 N to pound-force:
250 / 4.4482216152605 = 56.2022 lbf
Pound-Force to Newtons
Convert 100 lbf to newtons:
100 × 4.4482216152605 = 444.8222 N
Kilonewtons to Other Units
Convert 2.5 kN:
2.5 kN = 2500 N
2500 / 9.80665 = 254.9291 kgf
2500 / 4.4482216152605 = 562.0224 lbf
Mass to Weight Force
Calculate the weight force of a 50 kg mass under standard gravity:
W = 50 × 9.80665 = 490.3325 N
Dynes to Newtons
Convert 10 dyn to newtons:
10 × 0.00001 = 0.0001 N
Force Is Not Torque, Pressure, or Energy
| Quantity | Typical SI Unit | Relationship |
|---|---|---|
| Force | N | Push or pull |
| Torque or moment | N·m | Force multiplied by perpendicular lever arm |
| Pressure or stress | Pa = N/m2 | Force divided by area |
| Work or energy | J = N·m | Force applied through displacement |
Torque and energy can both be expressed using N·m, but they are different physical quantities and should not be treated as interchangeable.
Force Measurement Considerations
A converter changes units but does not improve measurement accuracy. Real force measurements may be affected by:
Load-cell calibration and traceability
Measurement range and overload history
Alignment and off-axis loading
Temperature effects and zero drift
Static versus dynamic loading
Fixture compliance and friction
Instrument resolution, repeatability, and uncertainty
Local gravity when force is generated using known masses
Significant Digits and Rounding
Exact conversion factors may produce many digits, but the input measurement still has limited precision. Retain sufficient digits during the conversion, then round the final result according to the measurement uncertainty and engineering purpose.
For example, a measured force reported as 250 N may not justify displaying 25.4929053248 kgf. A result such as 25.5 kgf or 25.49 kgf may better match the original precision.
Common Force Conversion Mistakes
Using kg as though it were kgf.
Using lb without determining whether mass or pound-force is intended.
Using local gravity when a defined kgf or lbf conversion requires standard gravity.
Confusing MN with mN because SI symbols are case-sensitive.
Using the incorrect legacy kip factor from the old table.
Confusing force in N with torque in N·m.
Confusing force with pressure or stress in N/m2.
Assuming a unit conversion removes load-cell uncertainty.
Rounding intermediate values before the final result.
Reporting more digits than the original measurement supports.
Applications
Load-cell and force-gauge measurements
Structural and mechanical engineering
Fastener preload and material testing
Actuator, spring, and hydraulic-cylinder calculations
Aerospace thrust and propulsion data
Product testing and manufacturing quality control
Converting legacy lbf or kgf specifications to SI
Frequently Asked Questions
What is the SI unit of force?
The SI unit of force is the newton, symbol N.
What is one newton?
One newton is the force that gives a one-kilogram mass an acceleration of one meter per second squared.
How many newtons are in one kilogram-force?
One kilogram-force equals exactly 9.80665 N.
How many newtons are in one pound-force?
One pound-force equals exactly 4.4482216152605 N.
How many newtons are in one kip?
One kip equals 1000 lbf or exactly 4448.2216152605 N.
Is kg a unit of force?
No. Kilogram is a unit of mass. Kilogram-force, kgf, is a non-SI unit of force.
What is the difference between lbf and lb?
lbf explicitly represents force. lb normally represents avoirdupois mass, although informal documents sometimes use lb for force when context is assumed.
Does a 1 kg mass always weigh 9.80665 N?
It has that weight force under standard gravity. Actual local gravitational acceleration varies, so local weight force can differ slightly.
Is N·m a force unit?
No. N·m is used for torque and also for energy when written as joule. Force alone is measured in newtons.
