Force Calculator

Enter any two of mass, acceleration and force and the third follows. The weight mode swaps acceleration for gravity and shows every planet at once, because the useful thing there is not one number but the fact that your mass is the same in all of them and only the weight moves.

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How this force calculator works

The first mode is Newton's second law: enter any two of mass, acceleration and force, and the third follows. The second mode is the special case everyone actually asks about, which is weight, where gravity supplies the acceleration and the answer changes depending on which world you are standing on. It shows every planet at once, because the point of that mode is not any single number but the fact that only one of the two quantities moves.

The formula

F = ma
W = mg
1 N = 1 kg m/s²
1 lbf = 4.448222 N (exactly 0.45359237 × 9.80665)

F is the net force in newtons, m the mass in kilograms and a the acceleration in metres per second squared. A newton is the force that accelerates one kilogram at one metre per second squared, which works out at roughly the weight of a small apple. The pound-force is defined as the weight of one pound of mass under standard gravity, which is why the conversion above is exact rather than measured.

Worked example

A 70 kg person. On Earth they weigh 70 × 9.80665 = 686.5 N, which is 154.3 lbf. On the Moon, where gravity is 1.625 m/s2, they weigh 113.8 N, about 25.6 lbf. On Jupiter they would weigh 1,735 N, roughly 390 lbf.

Their mass is 70 kg in all three places, and it never changed. That is the entire distinction between mass and weight in one line: mass is how much of them there is, weight is how hard a particular world pulls on it.

And the F = ma version. Pushing that same 70 kg person at 2 m/s2 takes 140 N, which is about a fifth of their body weight. That ratio is worth noticing, because it is why pushing a stalled car on level ground is possible and lifting it is not: accelerating something gently costs far less force than holding it up against gravity.

Mass and weight, and why the pound is a trap

In metric there is no confusion available: the kilogram is a mass, the newton is a force, and no one mixes them up because they are different words. US customary units are less kind, because the pound is used for both. A pound-mass is an amount of stuff; a pound-force is the weight of that stuff under standard gravity. They are numerically equal on Earth's surface and conceptually unrelated everywhere else.

The consequence bites engineering students hardest. If you insist on pounds for mass and pounds-force for force, F = ma stops working as written, because the units do not cancel. You need a conversion constant, gc = 32.174 lbm ft per lbf s2, sitting in the equation to make the books balance. The alternative, and the reason it exists, is the slug: a unit of mass defined so that one pound-force accelerates it at one foot per second squared, which makes F = ma work cleanly again. One slug is about 32.17 pounds of mass, or 14.59 kg. If you have ever wondered why a physics problem suddenly started talking about slugs, that is why, and this page will take them as an input.

Weightless is not gravity-free

Astronauts on the space station float, and the usual explanation, that there is no gravity up there, is simply wrong. At the station's altitude of roughly 400 km, Earth's gravity is still about 90% as strong as it is at the ground. If gravity had switched off, the station would not be in orbit; it would have left in a straight line years ago.

What has actually gone is not gravity but the floor. The station and everything in it are in continuous free fall, moving sideways fast enough that they keep missing the Earth. Everything falls together, so nothing presses on anything, and the sensation of weight, which is really the sensation of being pushed back by a surface, disappears. That is why the technical term is microgravity rather than zero gravity, and why the same weightlessness happens for a few seconds in a dropped lift or a parabolic aircraft. Weight in the everyday sense is not a property an object has; it is a description of what is pushing on it.

Frequently asked questions

How do I calculate force?

Multiply mass by acceleration. A 70 kg person accelerating at 2 m/s squared needs a net force of 140 newtons. The word net matters: F in the equation is the sum of everything acting, so a car pushed forward by its engine and back by drag accelerates on the difference rather than on the engine's contribution alone.

What is the difference between mass and weight?

Mass is how much material there is and how hard it is to accelerate; weight is the force a particular world's gravity exerts on it. A 70 kg person weighs 686.5 N on Earth, 113.8 N on the Moon and 1,735 N on Jupiter, and their mass is 70 kg in all three places. Mass is a property of the object, weight is a description of its situation.

How much would I weigh on the Moon or Mars?

About 16.6% of your Earth weight on the Moon and 37.9% on Mars, because their surface gravities are 1.625 and 3.721 m/s squared against Earth's 9.80665. Switch to weight mode above and it lists every planet at once. Your mass, which is what a balance actually measures, does not change at all.

What is a newton?

The force that accelerates one kilogram at one metre per second squared. It is a small unit in everyday terms, roughly the weight of a small apple, which is why forces in ordinary situations come out as hundreds or thousands of newtons. A pound-force is 4.448222 newtons, and that conversion is exact rather than measured, because the pound-force is defined as the weight of one pound of mass under standard gravity.

What is a slug and why does it exist?

A slug is the unit of mass that makes F = ma work in US customary units: one pound-force accelerates one slug at one foot per second squared. It exists because the pound is used for both mass and force, so writing F = ma with pounds on both sides does not balance dimensionally. The alternative is to keep pound-mass and insert a conversion constant of 32.174 into the equation. One slug is about 32.17 pounds of mass, or 14.59 kg.

Why are astronauts weightless if there is still gravity?

Because weight, in the sensation sense, is really the feeling of a surface pushing back at you. At the space station's altitude gravity is still about 90% as strong as at the ground, which is exactly why the station stays in orbit rather than flying off in a straight line. The station and everyone in it are in continuous free fall, moving sideways fast enough to keep missing the Earth, so everything falls together and nothing presses on anything. The proper term is microgravity, not zero gravity.

Does F = ma always work?

Only when the mass is constant. Newton actually stated the second law as force equals the rate of change of momentum, which reduces to ma only if m is not changing. For a rocket burning propellant, a raindrop growing as it falls, or anything else gaining or shedding mass, the momentum form is the correct one and F = ma quietly is not. It also breaks down near the speed of light, where relativistic mechanics takes over.

Why is pushing a car easier than lifting it?

Because accelerating something gently costs far less force than holding it up. Pushing a 70 kg object at 2 m/s squared takes 140 N, about a fifth of its 686 N weight. Lifting it means supplying the full 686 N just to stop it falling, before any upward acceleration at all. On level ground, friction and rolling resistance are all you have to beat, and those are usually a small fraction of the weight.

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