Force calculator: F = ma with working

The force here is the resultant force: add forces acting in the same direction and subtract opposite ones first. If a car's engine pushes with 4,000 N and friction and air resistance total 1,000 N, the resultant force is 3,000 N.

• Force: a 1,200 kg car accelerates at 2.5 m/s². $F = 1200 \times 2.5 = 3000$ N.
• Acceleration: a resultant force of 500 N acts on a 50 kg trolley. $a = 500 \div 50 = 10$ m/s².
• Mass: a force of 60 N gives an acceleration of 3 m/s². $m = 60 \div 3 = 20$ kg.

Masses given in grams need converting to kilograms first (divide by 1,000), which the calculator does for you.

1. First law: if the resultant force is zero, an object stays at rest or keeps moving at a constant velocity.
2. Second law: the acceleration is proportional to the resultant force and inversely proportional to the mass, $F = ma$.
3. Third law: when two objects interact, they exert equal and opposite forces on each other.

Our guide to Newton's laws of motion explains each with examples.

Weight is the force of gravity on a mass: $W = m \times g$, where $g$ is the gravitational field strength (about 9.8 N/kg on Earth). It's the same idea as $F = ma$ with the acceleration due to gravity. A 60 kg student has a weight of $60 \times 9.8 = 588$ N. Mass doesn't change from planet to planet; weight does.

• Using one force instead of the resultant force.
• Leaving mass in grams: 500 g is 0.5 kg.
• Confusing mass (kg) and weight (N).
• Forgetting direction: if the resultant force is backwards, the acceleration is negative (the object slows).

Practise with our Newton's second law questions and resultant force questions.

• Lifts: when a lift starts moving up, the cable tension is bigger than the weight, giving an upward resultant force and an upward acceleration.
• Rockets: as fuel burns, the mass falls, so the same thrust gives a bigger acceleration.
• Cars: a heavier car needs a bigger braking force to stop at the same rate, which is why loaded vans take longer to stop.
• Terminal velocity: a skydiver speeds up until air resistance equals weight; then the resultant force is zero and the speed stays constant.