Accelerating a car
plain
m = 1200 kg, a = 3 m/s²F = ma = 1200 · 3 = 3600 N, which is 3.6 kN. This is the net force: the engine has to push that much harder than the drag and friction holding the car back.
Force Calculator
Newton's second law, F = ma, and weight, W = mg, solved for any value.
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The force formula: Newton's second law
Newton's second law says the net force on an object equals its mass times its acceleration: F = ma. With m in kilograms and a in metres per second squared, F comes out in newtons, N. One newton is the force that gives 1 kg an acceleration of 1 m/s². Accelerating a 1200 kg car at 3 m/s² takes 1200 · 3 = 3600 N.
Weight is a force too, the pull of gravity on a mass, and it follows the same law with the acceleration of free fall: W = mg. On Earth g is 9.81 m/s², so a 70 kg person weighs 70 · 9.81 = 686.7 N. On the Moon g is 1.62 m/s² and the same person weighs 113.4 N. The mass stays 70 kg everywhere; only the weight changes.
The calculator has a tab for each. In the first, give two of force, mass and acceleration and it finds the third. In the second, give a mass for the weight, or a weight for the mass; g starts at 9.81 m/s² and you can change it for the Moon, another planet or a problem that uses 9.8, or clear it to find g from a weight and a mass. Grams, pounds, kilonewtons and pounds of force are converted to SI units first, and every step is shown.
What to notice
- F in F = ma is the net force, everything acting on the object added up with directions. Push a box with 50 N against 20 N of friction and the net force is 30 N.
- 1 N = 1 kg·m/s². A 100 g apple weighs about 0.98 N, roughly one newton.
- Mass is how much matter there is, in kilograms, and it is the same everywhere. Weight is a force, in newtons, and depends on g.
- Double the force on the same mass and the acceleration doubles; double the mass with the same force and it halves.
- A force has a direction. A negative answer means the force points the other way from the direction you chose as positive.
How to calculate force
Put the mass in kilograms
Grams divide by 1000, pounds multiply by 0.4536. 500 g is 0.5 kg.
Put the acceleration in m/s²
ft/s² multiply by 0.3048. For a weight, the acceleration is g: 9.81 m/s² on Earth.
Multiply
F = m · a. 1200 kg · 3 m/s² = 3600 N, which is 3.6 kN.
Rearrange for the other values
m = F/a and a = F/m. Leave blank the box you want and the calculator writes the rearranged formula before it puts the numbers in.
Weight of a 70 kg person around the solar system
W = mg with each world's surface gravity, rounded. The mass is 70 kg in every row; only g changes.
| Place | g | Weight |
|---|---|---|
| Moon | 1.62 m/s² | 113.4 N |
| Mars | 3.71 m/s² | 259.7 N |
| Venus | 8.87 m/s² | 620.9 N |
| Earth | 9.81 m/s² | 686.7 N |
| Jupiter | 24.79 m/s² | 1,735.3 N |
Worked examples
The mass from a force
plain
F = 20 N, a = 4 m/s²Leave the mass blank: m = F/a = 20 / 4 = 5 kg.
Your weight on Earth
plain
m = 70 kg, g = 9.81 m/s²In the weight tab, W = mg = 70 · 9.81 = 686.7 N, about 154.4 pounds of force.
The same person on the Moon
plain
m = 70 kg, g = 1.62 m/s²Change g to 1.62: W = 70 · 1.62 = 113.4 N, about a sixth of the weight on Earth, with the same 70 kg of mass.
Common mistakes
- Calling a mass a weight. 70 kg is a mass; its weight on Earth is 686.7 N. A bathroom scale shows kilograms because it divides by g for you.
- Using grams. 500 g is 0.5 kg; putting in 500 gives a force a thousand times too big.
- Using one force when several act. F = ma uses the net force, so add every force with its direction first.
- Confusing pounds with pounds of force. lb is a mass (0.4536 kg) and lbf is a force (4.448 N). A 1 lb mass weighs about 1 lbf on Earth.
- Using a different g from your course. Some problems round it to 9.8 or 10 m/s²; change the g box to match, or the answers will differ slightly.
- Leaving out the direction. A braking force on a car moving forward is negative if forward is positive, and F = ma then gives the negative acceleration of slowing down.
Force FAQ
What is the formula for force?
F = ma, Newton's second law: force equals mass times acceleration. With the mass in kilograms and the acceleration in m/s², the force is in newtons. 1200 kg at 3 m/s² needs 3600 N.
What is Newton's second law?
The net force on an object equals its mass times its acceleration, F = ma. A bigger force gives a bigger acceleration, and a bigger mass needs a bigger force for the same acceleration.
How do you calculate weight from mass?
Multiply by g, the acceleration of free fall: W = mg. On Earth g is 9.81 m/s², so 70 kg weighs 70 · 9.81 = 686.7 N. The answer is a force, in newtons.
What is the difference between mass and weight?
Mass is the amount of matter in an object, in kilograms, and it does not change from place to place. Weight is the force of gravity on that mass, in newtons, so it changes with g: 686.7 N on Earth and 113.4 N on the Moon for the same 70 kg.
What is a newton?
The SI unit of force: 1 N = 1 kg·m/s², the force that gives 1 kg an acceleration of 1 m/s². 1 kN is 1000 N, and 1 pound of force is about 4.448 N.
How do you find mass from force and acceleration?
Rearrange F = ma to m = F/a. A force of 20 N that gives an acceleration of 4 m/s² means a mass of 20 / 4 = 5 kg.
What is g on the Moon and other planets?
About 1.62 m/s² on the Moon, 3.71 on Mars, 8.87 on Venus and 24.79 on Jupiter, against 9.81 on Earth. Type any of them into the g box in the weight tab.
