Force Calculator
Solve Newton's second law for force, mass or acceleration, find weight on any planet, and work out friction and sliding on a flat surface or a slope.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Force Calculator?
This force calculator covers the three force problems that come up most. The first tab solves Newton's second law, F = ma, for whichever of force, mass and acceleration you do not know, with forces in newtons, kilonewtons, pounds-force, kilograms-force or dynes and acceleration in m/s², ft/s² or multiples of g.
The second tab turns a mass into a weight, W = mg, on Earth, the Moon, Mars, Venus, Jupiter or Mercury, and shows the weight on every body side by side.
The third tab handles friction on a flat surface or an incline. Pick a pair of surfaces from a textbook table of static and kinetic coefficients (or enter your own) and get the normal force, the friction force, the pull down the slope, whether the object slides on its own, its acceleration once sliding and the force needed to start and keep it moving.
- Newton's second law for force, mass or acceleration
- Weight on six planets and moons, or custom g
- Static and kinetic friction on flat surfaces and slopes
- Angle of repose and whether the object slides
- Textbook friction table and six force units
How to use the Force Calculator
- Pick a tab: F = m × a, Weight, or Friction and slopes.
- For F = ma, choose what to solve for, then enter the other two values with their units.
- For weight, enter a mass and choose a planet or custom gravity; the table shows the weight everywhere at once.
- For friction, enter the mass and slope angle (0 for flat), pick the surfaces or enter custom coefficients, and choose the force unit.
- Read the results and the plain-language verdict on whether the object slides, then copy or share the result.
Worked examples
Accelerating a car
Input
Mass 1,200 kg, acceleration 3 m/s²
Output
3,600 N (809.3 lbf); 0 to 100 km/h in 9.26 s
This is the net force. The engine must also overcome rolling resistance and drag, so it delivers more than 3.6 kN at the wheels.
Your weight on Mars
Input
Weight tab; 70 kg, Mars (3.71 m/s²)
Output
259.7 N, compared with 686.5 N on Earth
Mass stays 70 kg; the force on a scale falls to 38% of its Earth value.
Pushing a crate across a floor
Input
Friction tab; 50 kg, flat, custom μs 0.5, μk 0.3
Output
245.2 N to start it, 147.1 N to keep it moving
The jump from static to kinetic friction is why a heavy box lurches once it breaks free.
Wooden block on a 25° ramp
Input
20 kg, 25°, wood on wood (μs 0.25, μk 0.2)
Output
Slides on its own; accelerates at 2.37 m/s²
tan 25° = 0.466 is above μs, so static friction (44.4 N) cannot hold the 82.9 N down-slope pull. The angle of repose is 14.0°.
Background and insight
Newton's second law, published in the Principia in 1687, says the net force on a body equals the rate of change of its momentum, which for constant mass is F = ma. The SI unit is defined from it: one newton accelerates one kilogram at one metre per second squared. The force in the formula is the net force, after friction, drag and any opposing pushes are taken away.
Weight is the gravitational force on a mass, W = mg. Standard gravity g0 = 9.80665 m/s² is a defined constant, and the kilogram-force and pound-force are defined from it, so 1 kgf = 9.80665 N exactly and 1 lbf = 4.4482216152605 N exactly. Real g at sea level varies from about 9.780 at the equator to 9.832 at the poles because of the Earth's rotation and shape.
The friction model used here is the Amontons-Coulomb law: friction is proportional to the normal force, F = μN, and roughly independent of contact area and sliding speed. Static friction can rise up to μs N before motion starts; once sliding, the force drops to μk N. On a slope of angle θ the normal force is mg cos θ and the pull along the slope is mg sin θ, so an object starts to slide by itself when tan θ exceeds μs. That critical angle is the angle of repose.
Common use cases
Mechanics coursework
Check F = ma, weight and inclined-plane problems, including friction, with the formulas shown.
Moving heavy loads
Estimate the push needed to start and keep a crate, pallet or machine moving across a floor or up a ramp.
Ramp and chute design
Find the angle at which parts or materials start to slide on their own.
Unit conversion
Convert forces between newtons, kN, lbf, kgf and dynes, and accelerations between m/s², ft/s² and g.
Tips and limitations
- Friction coefficients are rough. Surface finish, contamination, humidity and temperature can change them by 50% or more, so test real surfaces when it matters.
- Coefficients above 1 are possible (soft rubber on rough surfaces); μ is not capped at 1.
- For a rope pulling at an angle, only the component along the surface moves the load, and the upward component reduces the normal force. This calculator assumes the push is parallel to the surface.
- Rolling objects such as wheels and carts use rolling resistance coefficients, typically 0.001 to 0.03, which are far smaller than sliding friction.
- In F = ma use mass in kilograms and acceleration in m/s² to get newtons; the unit pickers do this conversion for you.
Frequently asked questions
How do you calculate force?
Multiply mass by acceleration: F = m × a. A 1,200 kg car accelerating at 3 m/s² needs a net force of 3,600 N. Force is in newtons when mass is in kilograms and acceleration in m/s².
What is the difference between mass and weight?
Mass is the amount of matter, in kilograms, and is the same everywhere. Weight is the gravitational force on it, W = mg, in newtons; a 70 kg person weighs 686 N on Earth and 113 N on the Moon.
How many newtons is a kilogram?
A kilogram is a mass, not a force, but its weight under standard gravity is 9.80665 N, which is the definition of one kilogram-force (kgf).
How do you calculate the friction force?
Friction = μ × N, where N is the normal force. On a flat floor N = mg; on a slope N = mg cos θ. A 50 kg crate with μk = 0.3 needs 147 N to keep sliding.
What is the difference between static and kinetic friction?
Static friction holds an object still and can rise up to μs × N. Once it slides, kinetic friction μk × N takes over and is usually smaller, so it takes more force to start something moving than to keep it moving.
At what angle will an object slide down a slope?
When tan θ is greater than the static coefficient μs. The angle of repose is arctan(μs): 14° for wood on wood with μs = 0.25, 37° for steel on steel with μs = 0.74.
Is there an in-depth guide to the Force Calculator?
Yes. “Newton's Second Law, Weight and Friction: Solving Force Problems” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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