MotionLab

Force Calculator

F = m · a, in newtons.

Mass (kg)

Acceleration (m/s²)

Force (N)

98.1

F = m · a (Newton's second law)

What you entered

Mass (kg): 10Acceleration (m/s²): 9.81

1
Newton's second law: F = m × a
10 × 9.81= 98.1

Result

Force (N): 98.1

A 10kg mass accelerating at 9.81 m/s² requires 98.1 newtons of force.

Force from mass and acceleration

Newton's second law: force equals mass times acceleration. One newton accelerates one kilogram at one metre per second squared.

Mass (kg)	Acceleration (m/s2)	Force (N)	Context
1	1	1.00	Definition of the newton
0.5	20	10.00	Throwing a ball
10	9.81	98.10	Weight of a 10 kg mass
70	9.81	686.70	Weight of a 70 kg person
1000	2	2000.00	Car accelerating gently
1500	3	4500.00	Car accelerating briskly

Rows three and four use g as the acceleration, which turns the formula into weight: a 70 kg person weighs 686.7 newtons, not 70 - kilograms are mass and newtons are force, and conflating them is the most common mistake in the topic. On the Moon the same person has the same 70 kg mass but weighs about 114 N. The law applies to the net force: if several forces act, add them as vectors first, since an object moving at constant velocity has zero net force despite plenty of individual forces acting on it.

Newton's second law

Force equals mass times acceleration — a heavier object needs proportionally more force to achieve the same acceleration, and the same force accelerates a lighter object more than a heavier one.

Where this shows up

Engineering (how much force a motor or brake needs), sports science (launch force in throwing events), and basic physics problems all reduce to this single relationship.

Frequently asked questions

How much force does it take to accelerate a 70 kg person at 2 m/s²?

F = ma = 70 × 2 = 140 N. That's about the force of pushing a shopping cart up a moderate ramp. For comparison, Earth's gravity pulls on the same person with F = 70 × 9.81 = 686.7 N — their weight.

How is force different from energy?

Force is a push or pull measured in newtons (N). Energy is the capacity to do work, measured in joules (J). Force × distance = work/energy. You can apply a force without transferring energy (holding a weight stationary). See the work-energy calculator for energy problems.

What is a newton in everyday terms?

1 newton is roughly the weight of a small apple (about 100 grams in Earth's gravity). Your body weight in newtons is your mass in kg × 9.81. A 70 kg person weighs about 687 N. A strong punch delivers around 2,000–5,000 N of peak force.