Force calculator: F = ma and weight

Newton's second law says force equals mass times acceleration: F = ma, with force in newtons (N), mass in kilograms and acceleration in m/s². Making a 1200 kg car accelerate at 2.5 m/s² takes 1200 × 2.5 = 3000 N of resultant force. Weight is the same law with gravity as the acceleration, W = mg. This force calculator finds force, mass or acceleration, works out weight on Earth, the Moon and the planets, and handles driving and resistive forces together.

It opens on that car. Open the full force calculator over this page to try your own values.

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Force Calculator

Use F = ma to find force, mass, acceleration and weight

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How to use the force calculator

1. Under Calculate, choose F = ma, Weight or Resultant.
2. Choose what to find. F = ma: Force, Mass or Acceleration. Weight: Weight, Mass or Gravity. Resultant: Acceleration or Driving Force.
3. Type the values you know, with the unit for each. For gravity, leave the box blank for Earth (9.81 m/s²) or pick the Moon or a planet from its list.
4. Read the answer, the steps and the extra results: the acceleration in units of g, the speed after 10 s from rest, or the same mass's weight on other worlds.
5. The graph plots force against acceleration or weight against mass, and the resultant modes draw a force diagram.
6. To practise, press Random problem in the Practice section.

The force formula: F = ma

F is the resultant (net) force: all the forces on the object combined. One newton is the force that gives 1 kg an acceleration of 1 m/s², so 1 N = 1 kg m/s². The same force gives a lighter object a bigger acceleration, and a bigger force gives the same object a bigger acceleration.

Worked examples you can check in the calculator

Example 1: finding the force

A 1200 kg car accelerates at 2.5 m/s². F = 1200 × 2.5 = 3000 N. The calculator also expresses the acceleration as 0.255 g: about a quarter of the acceleration of free fall.

Example 2: finding the acceleration

A resultant force of 3000 N acts on the 1200 kg car. Choose Acceleration: a = 3000 ÷ 1200 = 2.5 m/s². The extra result says that from rest, after 10 s it would be doing 25 m/s, if the force stayed the same.

Example 3: finding the mass

A 3000 N resultant force gives an object an acceleration of 2.5 m/s². Choose Mass: m = 3000 ÷ 2.5 = 1200 kg.

Example 4: weight on Earth and the Moon

Choose Weight. A 70 kg person on Earth weighs W = 70 × 9.81 = 686.7 N. Pick the Moon, where g = 1.62 m/s², and the same person weighs 70 × 1.62 = 113.4 N, about a sixth as much. Their mass is still 70 kg: mass is the amount of matter, and weight is the pull of gravity on it. The calculator shows the weight on the Moon, Mars and Jupiter side by side.

Example 5: finding gravity

On another world, a 70 kg mass weighs 113.4 N. Choose Gravity: g = W ÷ m = 113.4 ÷ 70 = 1.62 m/s², the Moon's value.

When two forces act against each other, such as a driving force and friction, use the Resultant modes: the net force calculator guide works through them, including forces at angles. Try an F = ma question, then press Mark to check your answer in the Laws of Motion course.

Quick check

Mass vs weight

NASA's planetary fact sheet gives surface gravity as about 9.8 m/s² on Earth, 1.6 m/s² on the Moon and 3.7 m/s² on Mars. The calculator's values agree to that accuracy.

Common mistakes

• Using one force instead of the resultant in F = ma. Combine all the forces first.
• Giving weight in kg. Weight is a force, in newtons. Mass is in kg.
• Grams instead of kilograms. 500 g is 0.5 kg. Or choose grams as the unit in the calculator.
• Rearranging wrongly. a = F ÷ m and m = F ÷ a: the force is always on top.
• Thinking mass changes on the Moon. Only weight does.

Read next

Physics · MechanicsWeight equation: W = mg explained, with examplesThe weight equation W = mg: weight, mass and gravitational field strength, units, rearranging, weight versus mass, newtonmeters and worked examples.