Newton's Second Law: F = ma

Force is any interaction that changes the motion of an object. Newton's second law states that the net force on an object equals its mass times its acceleration: F = m × a. Force is measured in newtons (N), where 1 N is the force needed to accelerate 1 kilogram at 1 m/s². For a sense of scale, holding a medium apple against gravity takes roughly 1 N.

Solving for Any Variable

Because F = ma links three quantities, knowing any two gives you the third:

• Force: F = m × a — e.g. a 1,200 kg car accelerating at 3 m/s² requires a net force of 3,600 N.
• Mass: m = F / a — a 500 N force producing 2 m/s² of acceleration implies a 250 kg mass.
• Acceleration: a = F / m — 100 N applied to a 20 kg crate accelerates it at 5 m/s² (ignoring friction).

Advanced Force Types in This Calculator

• Weight (gravitational force): W = m × g. On Earth (g = 9.81 m/s²), a 70 kg person weighs 686.7 N. Weight changes with gravity; mass does not.
• Friction force: F = μ × N, where μ is the coefficient of friction and N is the normal force. Typical coefficients: rubber on dry concrete about 0.7, steel on steel about 0.6, ice on ice about 0.03.
• Centripetal force: F = m × v² / r, the inward force keeping an object moving in a circle. A 1,000 kg car rounding a 50 m curve at 15 m/s needs 1,000 × 225 / 50 = 4,500 N of centripetal force from tire grip.

Worked Example: Braking Force

A 1,500 kg car traveling at 20 m/s stops in 4 seconds. Its deceleration is 20 / 4 = 5 m/s², so the braking force is F = 1,500 × 5 = 7,500 N. Compare that with the car's weight of 1,500 × 9.81 = 14,715 N — the brakes are producing about half a g of deceleration.

Who Uses a Force Calculator?

• Students checking physics homework and exam prep problems.
• Engineers making quick estimates of loads, friction, and cornering forces.
• Teachers generating in-class examples with realistic numbers.
• Fitness and sports analysts estimating forces in sprints, jumps, and impacts.