Force formula: F = ma
Force = mass × acceleration, written F = m a. F is the resultant force in newtons (N), m is the mass in kilograms (kg) and a is the acceleration in metres per second squared (m/s²). This is Newton's second law. Every AQA, Edexcel and OCR specification has it as a recall equation, and it is printed on the exam sheet for each board.
Equation
F = m a
| Symbol | Quantity | Unit |
|---|---|---|
F | force | N |
m | mass | kg |
a | acceleration | m/s² |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | F = m a |
| AQA Combined Science (8464) | Recall | F = m a |
| Edexcel Physics (1PH0) | Recall | F = m a |
| Edexcel Combined Science (1SC0) | Recall | F = m a |
| OCR Gateway Physics A (J249) | Recall | F = m a |
| OCR Twenty First Century Physics B (J259) | Recall | F = m a |
Calculator: F = m a
Resultant force, in plain words
Most objects have several forces on them at once. A car has the push from its engine, air resistance against it, and friction in the wheels. The resultant force is what you get when you add them all up, taking direction into account.
F in this equation is always that resultant. If the forward push is 3000 N and the drag is 1000 N, the resultant is 2000 N forwards. That 2000 N is the number that goes into F = m a.
When the forces balance, the resultant is zero. Then the acceleration is zero too, and the object either stays still or keeps moving at a steady speed in a straight line.
What the boards print
All three boards print the same symbols, F = m a. The AQA wording is resultant force = mass × acceleration. Edexcel and OCR use force = mass × acceleration. It is a recall equation in AQA 8463 and 8464, Edexcel 1PH0 and 1SC0, and OCR J249 and J259.
You will still find it on the equation sheet in the exam. Boards have printed the recall list there since 2025, and the AQA equation page sets out that board's full list.
Rearranging and using it
- a = F ÷ m
- m = F ÷ a
The first form shows why a heavy lorry is slow to get going. The same force spread over a bigger mass gives a smaller acceleration.
F = m a sits at the centre of a group of equations. Weight is F = m a with the acceleration of free fall, which the weight equation covers. The acceleration equation gives you a from velocities and a time. For Higher tier, the force and momentum equation says the same thing in terms of how fast momentum changes.
Worked examples
F
- Change the mass to kilograms: 1.2 tonnes = 1200 kg
- F = m × a
- F = 1200 × 2
- F = 2400 N
2400 N
a
- a = F ÷ m
- a = 30 ÷ 40
- a = 0.75 m/s²
0.75 m/s²
m
- Change the force to newtons: 12 kN = 12 000 N
- m = F ÷ a
- m = 12 000 ÷ 4
- m = 3000 kg
3000 kg
Common mistakes
- Using one force when several act. Work out the resultant first, taking away forces that point the opposite way.
- Putting a mass in grams into the equation. A 500 g trolley must go in as 0.5 kg, or the force comes out 1000 times too big.
- Confusing mass with weight. A question that gives a weight of 50 N is not giving you a mass of 50 kg.
- Thinking a moving object must have a resultant force on it. A cyclist at a steady speed on a flat road has balanced forces.
Get quicker at pulling a or m out of F = m a in the Equation Rearranger.
Questions people ask
What is one newton?
One newton is the resultant force that gives a 1 kg mass an acceleration of 1 m/s². The unit is named after Isaac Newton.
Why is it harder to push a full shopping trolley?
A full trolley has more mass. With the same push, a = F ÷ m gives it a smaller acceleration, so it feels sluggish to start and to stop.