This calculator solves Newton’s second law, F = ma, in all three directions. Choose whether to solve for force, acceleration, or mass, set the other two values, and it works out the answer and shows the step. The box on the track carries a net-force arrow and accelerates so you can see what the number actually does.
How to use this F = ma calculator
- Pick what to solve for: Force, Acceleration, or Mass.
- Set the other two quantities with the sliders (or load a preset scenario).
- Read the answer, with the rearranged equation and numbers shown underneath.
- Watch the box: a bigger net force gives a longer arrow and quicker acceleration; a negative force pushes the arrow (and the box) the other way.
What F = ma means
Newton’s second law says the net force on an object equals its mass times its acceleration:
F = m × a
Force is in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²). One newton is exactly the force that accelerates a 1 kg mass at 1 m/s², so 1 N = 1 kg·m/s². The acceleration always points the same way as the net force.
The relationship is a direct proportion between force and acceleration, and an inverse proportion between mass and acceleration: double the net force and the acceleration doubles; double the mass and the acceleration halves.
Rearranging the equation: force, mass, or acceleration
One equation, three forms. Knowing any two quantities gives the third:
F = m × a | a = F / m | m = F / a
That is exactly what the three “Solve for” buttons do. If you would rather not memorise three formulas, memorise one picture:
Which form do I use?
Pick the row that matches what you already have.
| If you know | And you want | Use | Example |
|---|---|---|---|
| mass and acceleration | force | F = m × a | 7 kg × 4 m/s² = 28 N |
| force and mass | acceleration | a = F ÷ m | 12 N ÷ 4 kg = 3 m/s² |
| force and acceleration | mass | m = F ÷ a | 281.25 N ÷ 22.5 m/s² = 12.5 kg |
| mass, on Earth | weight (a force) | F = m × g | 5 kg × 9.8 m/s² = 49 N |
| weight in newtons | mass | m = F ÷ g | 49 N ÷ 9.8 m/s² = 5 kg |
The last two rows are not F = ma with different letters, they are F = ma with the acceleration already chosen for you. On Earth everything falls at about 9.8 m/s², so the force gravity pulls a mass with is m × 9.8. That is why “how many newtons is 5 kg” has an answer at all, and why the answer changes on the Moon.
The units, and where they go wrong
| Quantity | Symbol | SI unit | Written | In base units |
|---|---|---|---|---|
| Force | F | newton | N | kg·m/s² |
| Mass | m | kilogram | kg | kg |
| Acceleration | a | metre per second squared | m/s² | m/s² |
Read the first row and the last together and the whole unit system falls out: 1 N = 1 kg·m/s². A newton is not a separate idea, it is the name for whatever force accelerates one kilogram at one metre per second squared.
| Convert | Do this | Example | Why it matters |
|---|---|---|---|
| grams (g) to kilograms (kg) | ÷ 1000 | 250 g = 0.25 kg | F = ma needs kilograms. A mass in grams gives an answer 1000 times too big. |
| tonnes (t) to kilograms (kg) | × 1000 | 1.5 t = 1500 kg | Vehicle masses are usually quoted in tonnes. |
| centimetres per second squared (cm/s²) to metres per second squared (m/s²) | ÷ 100 | 450 cm/s² = 4.5 m/s² | Lab measurements often come out in centimetres. |
| kilonewtons (kN) to newtons (N) | × 1000 | 2.4 kN = 2400 N | Engine thrusts and structural loads are usually quoted in kilonewtons. |
| kilograms (kg) to newtons (N) of weight on Earth | × 9.8 | 5 kg = 49 N | A mass is not a force. Multiply by g = 9.8 m/s² to get the weight it pulls with. |
| newtons (N) of weight on Earth to kilograms (kg) | ÷ 9.8 | 98 N = 10 kg | Divide by g to go the other way. This is the only place 9.8 belongs. |
The multiplication in F = ma is the easy part. The units are where the marks go, because a mass in grams or an acceleration in cm/s² produces a perfectly confident answer that is wrong by a factor of a thousand or a hundred, and nothing in the arithmetic gives it away.
F = ma table
Rows are the mass in kilograms, columns are the acceleration in metres per second squared, and every cell is the net force in newtons.
| F in newtons | 1 m/s2 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 kg | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 2 kg | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
| 3 kg | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 |
| 4 kg | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 |
| 5 kg | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| 6 kg | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 |
| 7 kg | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 |
| 8 kg | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 |
| 9 kg | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 |
| 10 kg | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
It is a times table with units on it, which is all F = ma is once the units are right. A 7 kg mass at 4 m/s² needs 28 N; a 5 kg mass at 6 m/s² needs 30 N. For anything outside the grid, or anything with a decimal in it, use the calculator at the top.
Worked examples
- Solve for force. A 3 kg cart accelerates at 2 m/s². Net force F = m × a = 3 × 2 = 6 N.
- Solve for acceleration. A 1500 N net thrust acts on a 500 kg go-kart. a = F / m = 1500 / 500 = 3 m/s².
- Solve for mass. A 20 N net force gives 4 m/s². Mass m = F / a = 20 / 4 = 5 kg.
Set each one up in the calculator to see the same steps.
Net force, not just any force
The F in F = ma is the net force: the resultant after every force on the object is added as vectors. If several forces act, sum them first, then bring that single number here. Build and total those forces in the interactive free-body diagram, where you can see balanced versus unbalanced forces, then use the net force in this calculator.
Mass and weight are not the same
Mass (kg) is the amount of matter and never changes. Weight is the gravitational force on that mass, weight = m × g, which is just F = ma with the acceleration set to gravity (about 9.8 m/s² on Earth). The “Free fall (weight)” preset shows this: the net force on a falling 2 kg object is its weight, about 19.6 N.
Common mistakes with Newton’s second law
- A net force means acceleration, not steady speed. A constant net force gives constant acceleration, so the speed keeps changing. Zero net force is what gives constant velocity.
- More mass means less acceleration for the same force, not more. Mass resists changes in motion.
- Use the net force, not one single push. Subtract friction and other forces first.
- Acceleration is not velocity. Acceleration is how fast the velocity is changing (m/s²); an object can accelerate hard while momentarily at rest.
- Mass times speed is not a force. m × v is the momentum (kg·m/s), not F. A train rolling at a steady speed has enormous momentum and zero net force on it. The formula that looks nearly identical is measuring something else entirely.