What is force?
Force is a push or a pull, and physics gives it one clean definition: force is mass times acceleration. Newton wrote it down in 1687, and three and a half centuries later it is still the first equation anyone learns about motion.
The unit is the newton, written N. One newton is the force needed to accelerate one kilogram at one metre per second squared. That is precise and completely unhelpful as a mental picture, so here is the useful version: a newton is about the weight of a small apple in your hand — 102 grams under Earth's gravity. A 1 kg bag of sugar presses down with 9.8067 N. An average adult weighs somewhere between 600 and 900 N.
Force shows up in two kinds of question. The first is "how hard do I have to push this?" — a 1,200 kg car accelerating at 3 m/s² needs 3,600 N. The second is "what does this weigh, in newtons?" — the same multiplication, with gravity as the acceleration. A 70 kg person standing still is pressing on the ground with 686.4655 N.
Both are one multiplication. To calculate force you need exactly two numbers — a mass and an acceleration — and neither question should take more than a few seconds to answer.
How to use the Force Calculator
Two fields, no variable to pick first, no Calculate button. The page solves for force, which is what its name says it does.
- Type the mass into the first box and choose its unit — kilograms, grams, tonnes, pounds or ounces. The result appears as you type.
- Type the acceleration into the second box and choose its unit — m/s², ft/s², cm/s², g, or km/h per second.
- Want a weight instead? Tap Use gravity. It fills the acceleration with 9.80665 m/s² and tags the answer This is weight, so a weight becomes a one-field question.
- Read the force. Newtons are the headline; pounds-force, kilograms-force and dynes sit directly underneath, all four at once.
- Check the formula line. It substitutes your numbers — F = m × a = 70 kg × 9.80665 m/s² = 686.4655 N — so the working is on the page and not just the answer.
Switching a unit converts the number you already typed rather than reinterpreting it, so the answer holds still. Type 9.80665 in m/s², switch to ft/s², and the box reads 32.174 while the force stays exactly where it was.
Most pages that rank for this calculation open with a dropdown asking which variable you want to solve for, and several still submit a form and reload the page to perform one multiplication. A few put the working behind a study subscription — the calculator is the top of a signup funnel, not the product. This page has nothing to choose and nothing to join.
The formula behind F = m × a
F = m × a
F = force, in newtons (N)
m = mass, in kilograms (kg)
a = acceleration, in metres per second squared (m/s²)
The multiplication is easy. The units are where people lose marks.
F = m × a only produces newtons when mass is in kilograms and acceleration is in m/s². Put pounds in one side and you get a number with no meaningful unit attached to it. The Force Calculator converts everything to SI internally, multiplies once, and converts the answer back out — so you can type 150 lb and still get a correct figure in newtons.
Here is a full calculation. A 10 kg box is pushed so that it speeds up by 5 metres per second, every second.
- m = 10 kg
- a = 5 m/s²
- F = 10 × 5 = 50 N
- Same force in other units: 11.2404 lbf, 5.0986 kgf, 5,000,000 dyn
And the weight version, which is the more common reason people need this. A 70 kg person, with gravity doing the accelerating:
- m = 70 kg, a = 9.80665 m/s² (standard gravity)
- F = 70 × 9.80665 = 686.4655 N
- Which is 154.3236 lbf, 70 kgf, or 68,646,550 dyn
Notice the third figure: 70 kg of mass weighs exactly 70 kgf. That is not a coincidence, and it is the fastest sanity check you have. If the kilograms-force column doesn't match the mass you typed when gravity is the acceleration, you have a unit selected that you didn't mean to select.
What common masses weigh in newtons
Every row below uses standard gravity, 9.80665 m/s² — the figures the Force Calculator returns when you type a mass and tap Use gravity.
| Mass | Force (N) | Pounds-force (lbf) | Kilograms-force (kgf) |
|---|---|---|---|
| 0.5 kg | 4.9033 N | 1.1023 lbf | 0.5 kgf |
| 1 kg | 9.8067 N | 2.2046 lbf | 1 kgf |
| 60 kg | 588.399 N | 132.2774 lbf | 60 kgf |
| 70 kg | 686.4655 N | 154.3236 lbf | 70 kgf |
| 80 kg | 784.532 N | 176.3698 lbf | 80 kgf |
| 100 kg | 980.665 N | 220.4623 lbf | 100 kgf |
| 1 tonne (1,000 kg) | 9,806.65 N | 2,204.6226 lbf | 1,000 kgf |
The pattern is linear, which is worth internalising: every extra kilogram adds 9.8067 N. Doubling the mass doubles the force. There is no curve anywhere in this equation, which is why a rough answer is easy to do in your head — multiply by ten, then take a couple of percent back off.
Gravity is also not a universal constant. A 70 kg person weighs 686.4655 N on Earth and 113.4 N on the Moon, where acceleration due to gravity is about 1.62 m/s². Their mass never changed. If you want that comparison done for you across the solar system, the weight on other planets calculator covers Mercury through Neptune, plus Pluto, in one pass.
Newtons, pounds-force, kilograms-force and dynes
Four units, one quantity. They all describe the same push; they just count it against different reference points.
| Unit | Worth in newtons | What it actually is |
|---|---|---|
| newton (N) | 1 N | SI unit. The force that accelerates 1 kg at 1 m/s². |
| pound-force (lbf) | 4.4482 N | The weight of one pound under standard gravity. Standard in US engineering. |
| kilogram-force (kgf) | 9.8067 N | The weight of one kilogram under standard gravity. Also called the kilopond. |
| dyne (dyn) | 0.00001 N | The old CGS unit. 100,000 dyn make 1 N, which is why dyne figures look enormous. |
Read that from the other direction and one newton is 0.2248 lbf, 0.102 kgf, or 100,000 dyn.
The pound-force is defined as exactly one pound of mass under standard gravity, which produces a pleasing result: put 150 lb into the mass field and tap Use gravity, and you get 667.2332 N and exactly 150 lbf. The imperial figure comes back unchanged because pounds-mass and pounds-force are numerically identical at the Earth's surface — the single most common source of confusion in introductory mechanics, and the reason showing all four units at once is worth the line of screen it costs.
Every other calculator in this category makes you pick one unit from a dropdown and shows that one. If your textbook wants newtons and your worksheet wants pounds-force, you run the calculation twice.
Where a force calculation goes wrong
Mass isn't weight. Everyday English uses them interchangeably; physics does not. Your mass is a property of you, the same on the Moon. Your weight is a force, and it changes with gravity. Bathroom scales are labelled in kilograms, which is why so many people arrive here looking for a weight in newtons and are surprised it needs a second number at all.
A negative force is an answer, not an error. A 2 kg object at −3 m/s² gives −6 N, tagged Opposing the motion. The minus sign is direction: the force points the other way from whichever direction you called positive. Braking, drag and friction problems all live in negative numbers. A 1,200 kg car braking at −8 m/s² needs −9,600 N, and the sign is the whole point.
Zero acceleration gives zero force, and the Force Calculator shows 0 N rather than hiding. A mass of zero or less does hide the result, because there is no object to push. Very large numbers are caught and refused with a hint rather than rendered as Infinity or NaN, which is the kind of detail that looks small until a calculator hands you one in the middle of a homework problem.
F = m × a is the net force. It gives you the total force required, not the individual pushes. If friction is resisting the motion, your applied force has to cover both the acceleration and the friction. It also assumes constant mass — a rocket burning fuel breaks that assumption — and it stops being accurate at speeds near light. For a homework problem, a gym plate or a car, none of that matters.
Other forces have their own formulas. Spring force is k × x, friction is μ × N, and gravitational attraction between two bodies is G·m₁·m₂/r². None of them are m × a in disguise.
Related calculations
Force, mass and acceleration are the same equation rearranged, so each one gets its own page rather than hiding behind a solve-for menu. If you have a force and a mass and need the acceleration, use the acceleration calculator. If you have a force and an acceleration and need the mass, the mass calculator does that and handles mass unit conversion.
Acceleration usually arrives as a change in speed over time, and the speed calculator solves that side of the problem in mph, km/h, m/s, ft/s or knots. If the force in question is being applied at the end of a wrench, you want torque rather than force, and the Nm to ft-lbs converter covers the units mechanics actually use. For converting the mass itself before it reaches the formula, there is kg to lbs.
Frequently asked questions
How do I calculate force from mass and acceleration?
Multiply them. Mass in kilograms times acceleration in metres per second squared gives force in newtons: a 5 kg object accelerating at 2 m/s² needs 10 N. That is the entire method. The only real work is making sure your units are SI before you multiply, or letting the Force Calculator do the conversion for you.
How many newtons is 1 kg?
A kilogram isn't a force, so strictly the question has no answer — but what people mean is "what does 1 kg weigh?", and that is 9.8067 N under Earth's gravity. Kilograms measure mass; newtons measure force. The bridge between them is an acceleration, and on Earth that acceleration is 9.80665 m/s².
How do I calculate weight in newtons?
Multiply your mass in kilograms by 9.80665. A 70 kg person weighs 686.4655 N. That is what the Use gravity button does — it fills the acceleration field with standard gravity so you only type the mass, and it labels the answer This is weight so you know which quantity you're looking at.
Can I use pounds and feet per second squared?
Yes. The Force Calculator's mass dropdown takes kg, g, tonnes, pounds and ounces; the acceleration dropdown takes m/s², ft/s², cm/s², g and km/h per second. Everything is converted to SI internally before the multiplication, so mixing a mass in pounds with an acceleration in m/s² is fine and still gives a correct answer in newtons.
What force does a 1,200 kg car need to accelerate at 3 m/s²?
3,600 N — which is 809.3122 lbf, or 367.0978 kgf. That is the net force at the wheels, so the real engine output has to be higher to also overcome rolling resistance and air drag. Brake in the other direction at −8 m/s² and the figure is −9,600 N, with the minus sign carrying the direction.
Does F = m × a work for gravity, friction or springs?
Only indirectly. F = m × a tells you the net force producing an acceleration. Gravitational attraction between two bodies uses G·m₁·m₂/r², spring force uses k × x, and friction uses μ × N. This page deliberately solves one equation rather than bundling five behind a mode picker.
Is the Force Calculator free, and does it need an account?
It's free, there's no sign-up, and nothing you type leaves your browser — the multiplication happens on your device and closing the tab clears it. There's no trial, no paywalled working, and no interstitial between the inputs and the answer. Microapp gives 10% of every dollar it earns to charity, off the top, audited quarterly, and this tool is the full version of itself rather than a teaser for a paid one.