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    F = ma Calculator (Newton's Second Law)

    GCSE PhysicsAQAEdexcelOCRFoundation & Higher

    Find the resultant force, mass or acceleration using F = m × a. Enter grams, tonnes or kilonewtons and the solver converts for you.

    Quick answer

    Resultant force = mass × acceleration. Use kg and m/s² to get newtons. For example, a 1200 kg car accelerating at 2.5 m/s² needs a resultant force of 1200 × 2.5 = 3000 N. Use the overall (resultant) force, not just one force.

    By Engr. Mehmood Kakar · Updated

    F = m × a
    Find:

    Simulation

    Force, mass and acceleration

    A resultant force pushes a trolley from rest. The dots mark its position every half second: the gaps grow faster for a bigger force or a smaller mass.

    20 N
    5 kg

    Acceleration is proportional to the resultant force and inversely proportional to the mass. Double the force: double the acceleration. Double the mass: half the acceleration.

    Put these numbers in the calculator above

    How to use F = ma

    Newton's second law says that the acceleration of an object is directly proportional to the resultant force on it, and inversely proportional to its mass:

    resultant force = mass × acceleration

    • F is the resultant force in newtons (N)
    • m is mass in kilograms (kg)
    • a is acceleration in m/s²

    A 1200 kg car accelerating at 2.5 m/s² needs a resultant force of 1200 × 2.5 = 3000 N.

    The force must be the resultant force: the overall force once all the forces are combined. If a car's engine gives a 4000 N driving force and drag and friction add up to 1000 N, the resultant force is 4000 − 1000 = 3000 N, and that is the value to use.

    A bigger mass needs a bigger force for the same acceleration. This is also why a 1 N force is defined as the force that gives a 1 kg mass an acceleration of 1 m/s².

    Common mistakes that cost marks

    1. Using one force instead of the resultant. Subtract opposing forces like drag and friction first.
    2. Leaving mass in grams. 800 g is 0.8 kg.
    3. Using weight instead of mass. m is mass in kg. If you are given weight, divide by g first.
    4. Dividing the wrong way. a = F ÷ m. A heavier object accelerates less for the same force.

    Practice questions

    Try each one on paper first, then reveal the worked answer.

    Q1A 1200 kg car accelerates at 2.5 m/s². Calculate the resultant force on it.[2 marks]
    1. F = m × a
    2. F = 1200 × 2.5
    3. F = 3000 N
    Q2A resultant force of 600 N gives an object an acceleration of 4.0 m/s². Calculate its mass.[3 marks]
    1. Rearrange: m = F ÷ a
    2. m = 600 ÷ 4.0
    3. m = 150 kg
    Q3A resultant force of 24 N acts on an 800 g trolley. Calculate its acceleration.[3 marks]
    1. Rearrange: a = F ÷ m
    2. Convert: m = 800 ÷ 1000 = 0.80 kg
    3. a = 24 ÷ 0.80
    4. a = 30 m/s²

    Endless practice

    A new question every time, marked instantly. Work it out on paper, then type your answer.

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    Frequently asked questions

    What is Newton’s second law?

    The acceleration of an object is directly proportional to the resultant force on it and inversely proportional to its mass. As an equation: resultant force = mass × acceleration (F = ma).

    What is a resultant force?

    The single force that has the same effect as all the forces acting on an object combined. If the forces are balanced, the resultant force is zero and the object does not accelerate.

    How do I find acceleration from F = ma?

    Divide the resultant force by the mass: a = F ÷ m.

    What is 1 newton?

    The force that gives a mass of 1 kg an acceleration of 1 m/s².