About the Force Calculator
A force is a push or a pull, and Newton's second law tells you exactly what it does: a net force on an object makes it accelerate, in proportion to the force and in inverse proportion to the object's mass. Written as F = m × a, it is probably the most used equation in physics, behind everything from designing car engines and lifts to launching rockets and calculating the load on a bridge.
This force calculator solves F = ma for force, mass or acceleration. It accepts mass in kilograms, grams, tonnes, pounds or ounces; acceleration in m/s², ft/s² or multiples of g; and force in newtons, kilonewtons, pounds-force, kilogram-force or dynes. It converts everything to SI units, shows the answer in several units, and tells you what mass the same force would hold up against gravity.
How to Use the Force Calculator
Choose Find force, Find mass or Find acceleration.
Enter the two values you know and choose their units.
To find an object's weight, enter its mass and an acceleration of 1 g.
The Formula
F = m × a m = F ÷ a a = F ÷ m
F in newtons (N), m in kilograms (kg), a in metres per second squared (m/s²)
1 N = 1 kg·m/s²
1 lbf ≈ 4.4482 N 1 kgf = 9.80665 NStep-by-Step Examples
Accelerating a car. What force accelerates a 1,000 kg car at 3 m/s²?
F = 1,000 × 3 = 3,000 N = 3 kN ≈ 674.43 lbfWeight. What does a 70 kg person weigh in newtons?
F = 70 × 9.80665 = 686.47 N ≈ 154.32 lbfFinding acceleration. A net force of 500 N acts on a 50 kg mass.
a = 500 ÷ 50 = 10 m/s² (about 1.02 g)Finding mass. A force of 100 N gives an acceleration of 2 m/s².
m = 100 ÷ 2 = 50 kgNewton's Three Laws
Newton's first law says an object stays at rest, or keeps moving in a straight line at a steady speed, unless a net force acts on it. The second law, F = ma, says how much it accelerates when a force does act. The third law says forces come in pairs: when you push on a wall, the wall pushes back on you with an equal and opposite force. Together they describe almost all everyday motion, and they were published by Isaac Newton in 1687.
Net Force
The F in F = ma is the net force — the sum of every force on the object, taking direction into account. A car's engine may push forward with 4,000 N while air resistance and rolling resistance push back with 1,000 N; the net force of 3,000 N is what accelerates the car. When the forces balance, the net force is zero and the object moves at a constant velocity, which is why a car cruising at a steady speed on a flat road still needs its engine to overcome drag. Forces pointing in opposite directions are given opposite signs.
Mass and Weight
Mass is the amount of matter in an object, measured in kilograms, and it is the same everywhere. Weight is the force of gravity on that mass, measured in newtons, and it depends on where you are. On Earth, standard gravity is 9.80665 m/s², so a 70 kg person weighs about 686 N. On the Moon, where gravity is about a sixth as strong, the same person would weigh only about 113 N, although their mass would not change. In everyday speech "weight" is often given in kilograms, which is really mass.
Units of Force
The newton is the SI unit: the force that accelerates one kilogram at one metre per second squared. It is a small unit — roughly the weight of a small apple. The kilonewton is used for larger loads, such as the forces on bridges or car engines. The pound-force is the weight of one pound under standard gravity, about 4.4482 N, and is common in the United States. The kilogram-force is the weight of one kilogram, exactly 9.80665 N, and the dyne is a tiny unit from the older CGS system, one hundred-thousandth of a newton.
Force in Practice
Engineers use F = ma to size motors, brakes and structures. A lift must provide enough force to support its load and accelerate it upwards, so the cable tension is greater than the load's weight while the lift speeds up. Car safety systems depend on it too: the force on a passenger in a crash equals their mass times the deceleration, which is why seat belts, crumple zones and airbags are designed to spread the stop over a longer time and distance, reducing the deceleration and so the force.
Understanding Your Result
The headline is the force, mass or acceleration you asked for, in your chosen unit.
The force in other units line gives the force in N, kN, lbf and kgf.
The mass and acceleration line restates both, with the acceleration in g.
The weight equivalent line shows the mass the same force could hold up against Earth's gravity.
When Should You Use This Calculator?
Use it for physics homework on Newton's laws.
Use it to convert a mass into its weight in newtons or pounds-force.
Use it to estimate the force needed to accelerate a vehicle or load.
Common Mistakes
Using grams instead of kilograms. Newtons need kilograms.
Forgetting other forces. F = ma uses the net force, after friction and drag.
Confusing mass and weight. Mass is in kg; weight is a force in N.
Mixing up acceleration units. 1 g is 9.80665 m/s², not 1 m/s².