Work out any one of force, mass or acceleration from the other two, or the weight of a mass under four different gravities. Newtons, kilonewtons, kilogram-force and pounds-force, all four on every answer.
How many newtons does 10 kg weigh on Earth?
Work out any one of force, mass or acceleration from the other two, or the weight of a mass under four different gravities. Newtons, kilonewtons, kilogram-force and pounds-force, all four on every answer.
A mass of 10 kg is the same 10 kg anywhere in the universe. What changes with location is its weight, which is a force, and on Earth that force is the mass multiplied by the standard gravity of 9.80665 m/s². The result below is in newtons, with the same figure repeated in kilogram-force and in pounds-force, because a specification sheet will quote whichever of the three its author grew up with.
The distinction matters more than it sounds. A bathroom scale cannot weigh you in kilograms and does not try: it measures the force you press into it, then divides by Earth gravity and shows the mass that force implies. Take the same scale to the Moon and the reading would be wrong while your 10 kg sat there unchanged. Switch the calculator below to the Moon, Mars or Jupiter to see how far apart the two ideas can get.
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Three quantities, any two of them, and the third one falls out
Most of the trouble with F = ma is not the algebra. It is that the mass on the label is in pounds, the force in the specification is in kilogram-force, the acceleration in the article is quoted in g, and the formula wants all three in SI at once. This tool takes any two of force, mass and acceleration and returns the third, and it also does weight, which is the same law with gravity supplying the acceleration.
Eight situations, and the number each one needs
A car pulling away from the lights
Known: mass1400 kg, acceleration 3 m/s².Result: 4,200 N of net drive force.
The same car braking hard
Known: mass1400 kg, acceleration -8 m/s².Result: -11,200 N. The minus is the whole point: the force points backwards, and its size is what the tires have to find in the road surface.
Holding a box off the ground
Known: mass20 kg, weight mode, Earth.Result: 196.13 N, which is what your arms supply just to stop it falling. Lifting it faster costs more; holding it still costs exactly this.
How much can one person shift?
Known: force500 N, wanted acceleration 2 m/s².Result: 250 kg. On wheels and level ground, one steady shove brings a quarter of a metric ton up to 2 m/s, a brisk walking speed of 4.5 mph, in one second.
Why you feel heavier in a rising elevator
Known: mass80 kg, acceleration 11.30665 m/s², which is gravity plus the elevator's own 1.5.Result: 904.53 N through the floor, against 784.53 N standing still. The extra 120 N is what the sensation actually is.
What an airbag is up against
Known: mass75 kg, deceleration 294.2 m/s², which is 30 g.Result: 22,065 N spread across the chest, and the reason the bag has to be soft and wide rather than merely present.
The same body somewhere else
Known: mass70 kg, weight mode, the Moon.Result: 113.40 N against 686.47 N at home. The mass never changed; only the gravity did.
Sizing a drone that has to climb
Known: force6000 N of thrust, mass 500 kg.Result: 12 m/s², or 1.224 g. Since it needs 1 g just to hover, only the remainder is climb.
What goes in each box
- Which quantity you are missing - force, mass, acceleration, or weight. Only the fields that matter to your choice stay on screen.
- Mass unit - kilograms, grams, metric tons or pounds. One pound is exactly 0.45359237 kg, and the conversion runs before the physics rather than after it.
- Force unit - newtons, kilonewtons, kilogram-force or pounds-force. It appears only in the two modes where you type a force in, because the answer is printed in all four units whatever you pick.
- The two numbers you have - mass and acceleration, or force and one of the other two. A negative acceleration means slowing down along your chosen direction, and the force comes back negative with it.
- Gravity, in weight mode only - Earth, the Moon, Mars or Jupiter. The mass field stays the same, because mass does not care where it is.
- Read the result - the headline tile holds the quantity you asked for, the second tile the same force in other units, and the table underneath shows where it sits between an apple and an airliner.
Four units for one force, and where each is still used
A newton is not an intuitive size: it is roughly the weight of a small apple. That is why three other units survive alongside it, and why a specification quoting 428 kgf and one quoting 4.2 kN can be describing exactly the same thing.
| Unit | In newtons | 1 N equals | Where you meet it |
|---|---|---|---|
| Newton (N) | 1 | 1 N | Physics, everything SI |
| Kilonewton (kN) | 1,000 | 0.001 kN | Structural loads, crash ratings, winches |
| Kilogram-force (kgf) | 9.80665 | 0.10197 kgf | Older European engineering, some torque tables |
| Pound-force (lbf) | 4.4482216152605 | 0.22481 lbf | US practice, thrust ratings, torque wrenches |
Both of the gravitational units are defined against 9.80665 m/s², the standard gravity fixed by agreement rather than measured anywhere in particular. That is why a kilogram-force is not a kilogram and a pound-force is not a pound: each is what that mass would weigh under that exact acceleration, and the calculator uses the same constant everywhere so the four columns can never drift apart.
Weight is a force. Mass is not.
In shops the two words are interchangeable and nothing goes wrong. In the second law they are different quantities with different units, and mixing them is the single most common reason an answer comes out roughly ten times too big or too small. Mass is how much matter there is, measured in kilograms, and it is the same everywhere. Weight is the force gravity applies to that mass, measured in newtons, and it changes with where you are standing.
| Where | Gravity (m/s²) | Mass of a person | Their weight | Against Earth |
|---|---|---|---|---|
| Earth | 9.80665 | 70 kg | 686.47 N | 1.000 |
| The Moon | 1.62 | 70 kg | 113.40 N | 0.165 |
| Mars | 3.71 | 70 kg | 259.70 N | 0.378 |
| Jupiter, at the 1 bar level | 24.79 | 70 kg | 1,735.30 N | 2.528 |
The mass column does not move, and that is the entire lesson. Jupiter has no surface to stand on, so its figure is the one quoted at the pressure level where the atmosphere reaches one bar; the other three are surface values from the NASA planetary fact sheets. A bathroom scale, incidentally, measures force and then divides by Earth gravity to show you a mass, which is why it would read wrong on the Moon while your mass sat there unchanged.
Where readers usually push back
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Calculator verified by the LiczGrupa.pl team
Content, formulas and results have been reviewed for accuracy and relevance by our team of specialists.
Reviewed by: Natalia Skrzek