Force Calculator
This force calculator works five ways: from mass and acceleration (F = m · a), as weight, from pressure and area, as spring force or with the lever law. A 1200 kg car accelerating at 2.5 m/s² needs 3000 N – converted to kN, kgf and lbf as well.
Example: Method: From mass and acceleration (F = m · a) · Mass m 1,200 kg · Acceleration a 2.5 m/s² → Force: Force F = 3,000 N. Source: Wikipedia – Newtonsche Gesetze (F = m · a). Updated: .
How it is calculated
Force is the product of mass and acceleration: F = m · a, measured in newtons (N). 1 N accelerates a mass of 1 kg at 1 m/s². Depending on the task, only the source of the acceleration or of the force changes.
The five cases in the calculator
- F = m · a: the force needed to accelerate a mass – when starting, braking or lifting.
- Weight F = m · g: with g = 9.80665 m/s² (standard gravity) 80 kg weigh about 785 N. On the Moon at 1.62 m/s² it would be only about 130 N.
- F = p · A: the force of a cylinder or piston. 6 bar on 50 cm² gives 3000 N – the standard case in hydraulics and pneumatics. The calculator converts bar and cm² to pascals and m² for you.
- Spring force F = k · x: Hooke’s law holds in the elastic range: twice the extension, twice the force.
- Lever law: effort times effort arm equals load times load arm. A longer lever arm reduces the force needed in the same ratio.
Units
The SI unit is the newton. 1 kN = 1000 N; the kilogram-force (kgf) is obsolete, 1 kgf = 9.80665 N, and in the US the pound-force is common, 1 lbf ≈ 4.448 N. For work, energy and power see the kinetic energy calculator, and for falling objects the free fall calculator.
Frequently asked questions
How do you calculate a force?
With F = m · a: mass in kg times acceleration in m/s² gives force in newtons. For 1200 kg and 2.5 m/s² that is 3000 N.
How do you calculate force from pressure and area?
F = p · A. Pressure in pascals times area in m² gives newtons. At 6 bar (600,000 Pa) and 50 cm² (0.005 m²) it is 3000 N.
How do I convert newtons to kilograms?
Newtons divided by 9.80665 give the mass in kg that has this weight on Earth. 98 N correspond to about 10 kg. Strictly speaking, though, newtons and kilograms are different quantities.
What does the lever law say?
In balance, effort times effort arm equals load times load arm. Quadruple the effort arm and you need only a quarter of the force.
What is the spring constant?
It states how much force a spring produces per millimetre of travel. With k = 2.5 N/mm and 12 mm of extension the force is 30 N.
Sources and legal basis
- Wikipedia – Newtonsche Gesetze (F = m · a)
- Wikipedia – Hookesches Gesetz (Hooke's law)
- Wikipedia – Hebelgesetz
- BIPM – SI-Brochure: standard acceleration of gravity 9.80665 m/s² and kilopond/pound-force
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