Compute force, mass, or acceleration with Newton’s second law — every step shown, correct SI units throughout. Free and mobile-friendly.
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Force is what changes motion: it speeds things up, slows them down, or bends their path. Newton’s second law ties force to the two things it depends on — mass and acceleration — in one of the simplest and most powerful equations in physics: F = ma. Our free Force Calculator solves this equation in any direction: give it mass and acceleration to get force, or rearrange to find a missing mass or acceleration, with the unit bookkeeping handled for you.
The SI unit of force is the newton (N): one newton accelerates one kilogram at one meter per second squared. It is a small unit by everyday standards — an apple weighs about one newton — which is why car engines are rated in thousands of newtons and rocket thrusts in millions. Getting comfortable with newtons, kilograms, and m/s² is the gateway to all of mechanics.
Below you will find more than a button: an explanation of what force really is (and is not), the three rearrangements of F = ma, worked examples from sports to spaceflight, the unit-conversion traps that ruin homework, and the classic misconceptions — like confusing mass with weight — that this law exists to clear up.
Mass (m, kilograms) measures how much matter an object contains — and equivalently, how strongly it resists changes in motion (its inertia). Mass does not change when you travel: a 70 kg astronaut is 70 kg on Earth, on the Moon, and in deep space. Weight, by contrast, is a force — mass times local gravity — so the astronaut weighs 686 N on Earth but only about 114 N on the Moon. Confusing the two is the original sin of mechanics homework.
Acceleration (a, m/s²) is the rate at which velocity changes. A car going from 0 to 27 m/s (about 60 mph) in 6 seconds accelerates at 4.5 m/s². Acceleration has a direction: speeding up, slowing down, and turning are all accelerations, because velocity is a vector. Newton’s law says the net force — the vector sum of all pushes and pulls — equals mass times this acceleration.
Force (F, newtons) is therefore the thing that produces acceleration in proportion to mass. Double the force on the same mass and you double the acceleration; double the mass under the same force and the acceleration halves. The law F = ma is a vector equation really (F⃗ = m·a⃗): force and acceleration point the same way, which is why a sideways force curves a trajectory instead of just changing speed.
F = m × a • m = F ÷ a • a = F ÷ m
SI units: F in newtons (N), m in kilograms (kg), a in meters per second squared (m/s²). 1 N = 1 kg·m/s². Convert grams → kg (÷1000) and km/h → m/s (÷3.6) before computing.
A 10 kg box accelerates at 2 m/s². The net force: F = 10 × 2 = 20 N. That is roughly the weight of a 2-liter bottle of water — a gentle push. Note the word net: if friction pushes back with 6 N, you must push with 26 N to achieve a 20 N net force. F = ma always uses the net force.
A rocket engine produces 500,000 N of thrust and the rocket accelerates at 5 m/s² off the pad (after accounting for gravity separately). Its mass: m = F ÷ a = 500,000 ÷ 5 = 100,000 kg (100 tonnes). Rearranging the law is routine in engineering: thrust is known from the engine spec, acceleration from the flight plan, mass is the unknown to verify.
A 1,500 kg car’s engine delivers a net forward force of 6,000 N. Acceleration: a = F ÷ m = 6,000 ÷ 1,500 = 4 m/s² — about 0.4 g, a brisk but ordinary launch. Time to reach 27 m/s (60 mph): t = v ÷ a = 27 ÷ 4 ≈ 6.75 s, matching real family-sedan figures. One law, chained with one kinematics fact, predicts the 0–60 time.
You (70 kg) stand on a bathroom scale in an elevator accelerating upward at 2 m/s². What does the scale read? The scale measures the normal force pushing up on you. Forces on you: gravity pulls down with mg = 70 × 9.8 = 686 N; the floor pushes up with N. Net force must equal ma upward: N − 686 = 70 × 2 = 140, so N = 826 N — the scale reads about 84 kg. You feel heavier because the floor must both support your weight and accelerate you.
Now the cable snaps and you fall freely (ignoring air). Acceleration is 9.8 m/s² downward, so N − 686 = 70 × (−9.8) gives N = 0 N — weightlessness. Your mass never changed; the force the scale measures vanished. Astronauts in orbit feel the same thing permanently: they are in continuous free fall around Earth, so scales read zero while mass stays put. F = ma explains both the heavy feeling and the floating.
F = ma is the second of Newton’s three laws of motion (1687). The first law — objects keep their velocity unless a net force acts — is really the special case a = 0. The third — every action has an equal, opposite reaction — explains where forces come from: the floor pushes up on you exactly as hard as you push down on it. Together they describe all everyday mechanics, from walking (you push Earth backward; Earth pushes you forward) to rockets (exhaust pushed down; rocket pushed up).
The law survived 200 years unchallenged until Einstein. Relativity refines it at near-light speeds, where mass effectively grows with velocity, and quantum mechanics replaces trajectories with probabilities at atomic scales. But for cars, balls, buildings, and spacecraft, F = ma remains exact for all practical purposes — engineers still design bridges with Newton, not Einstein.
A subtle point: F = ma in its most general form is F = dp/dt — force equals the rate of change of momentum (p = mv). For constant mass this reduces to ma, but the momentum form also handles rockets losing mass as they burn fuel, where ma alone would mislead. When mass changes, think momentum.
A 1,000 kg car brakes with a net force of 8,000 N. Deceleration: a = 8,000 ÷ 1,000 = 8 m/s² (about 0.8 g — hard braking). From 25 m/s, stopping takes t = 25 ÷ 8 ≈ 3.1 s over d = v² ÷ (2a) = 625 ÷ 16 ≈ 39 m. Double the speed and the distance quadruples — the v² law that makes speeding so dangerous.
A 70 kg astronaut on Mars (g = 3.7 m/s²): weight W = mg = 70 × 3.7 = 259 N, versus 686 N on Earth. Mass unchanged at 70 kg. This is why astronauts bound gracefully on the Moon while their inertia — the effort to start or stop moving — feels exactly Earth-normal.
What net force accelerates a 2,000 kg truck at 3 m/s²? (F = 2,000 × 3 = 6,000 N.)
A 45 N net force acts on a 15 kg sled. Find the acceleration. (a = 45 ÷ 15 = 3 m/s².)
A 1,200 N force produces an acceleration of 0.5 m/s². What is the mass? (m = 1,200 ÷ 0.5 = 2,400 kg.)
In a crash, a driver’s body must go from 15 m/s to zero. Without an airbag the stop takes ~0.02 s against the steering wheel: a = Δv ÷ Δt = 15 ÷ 0.02 = 750 m/s² (≈ 76 g), so a 70 kg torso feels F = 70 × 750 = 52,500 N — unsurvivable. An airbag stretches the stop to ~0.2 s: a = 75 m/s², F = 5,250 N — still violent, but survivable. Same Δv, ten times the time, one-tenth the force.
This is F = ma read as F = m·Δv/Δt: force is inversely proportional to stopping time. Crumple zones, helmets, and padded dashboards all exploit the same trade — buy milliseconds, save lives. Every safety engineer’s first calculation is this one.
The Force Calculator applies Newton’s second law F = ma in SI units (newtons, kilograms, m/s²), solving for any one variable: F = m×a, m = F÷a, a = F÷m. Key facts: use net force (vector sum); mass is intrinsic while weight W = mg varies with gravity; 1 N = 1 kg·m/s²; convert grams to kg before computing.
It states that the net force on an object equals its mass times its acceleration: F = ma. Double the force, double the acceleration; double the mass, halve the acceleration. It is the core quantitative law of classical mechanics.
The SI unit of force: one newton (1 N) accelerates a 1 kg mass at 1 m/s². An apple weighs roughly 1 N; a car engine produces thousands of newtons.
Multiply: F = m × a. A 10 kg box accelerating at 2 m/s² needs F = 10 × 2 = 20 N of net force. Keep mass in kg and acceleration in m/s².
Mass (kg) is how much matter an object has — it never changes. Weight (N) is the gravitational force on that mass, W = mg, and changes with gravity: 70 kg weighs 686 N on Earth but 259 N on Mars.
Force is a vector, so its sign indicates direction. A “negative” force just points opposite your chosen positive axis — like friction opposing motion. The magnitude is always positive.
Because opposing forces cancel. Pushing a box with 26 N against 6 N of friction gives a net 20 N, and only that net 20 N goes into ma. Summing forces with correct signs comes before any F = ma calculation.
Yes — it is universal for everyday speeds. Rockets are the purest example: thrust (force) accelerates the spacecraft’s mass. In orbit, astronauts feel weightless not because forces vanished but because everything falls together.
Using grams instead of kilograms (divide by 1000), using km/h instead of m/s (divide by 3.6), and plugging weight in newtons where mass in kilograms belongs. Convert to kg, m, s first.
Cite this page as: Force Calculator. Sigma Calculator. Retrieved October 11, 2026, from https://sigmacalculator.net/math-calculators/force-calculator/
Last updated: October 11, 2026