Newton's second law calculator
Calculate force, mass or acceleration using Newton's second law F = m · a.
Calculations are based on Estonia's tax rates in force for 2026. Results are informational.
Last updated: 2026-06-03
What is Newton's second law?
Newton's second law states that the force on a body equals its mass times acceleration: F = m · a. Knowing two values, you can calculate the third: m = F / a, a = F / m.
How it is calculated
Formula
Newton's second law F = m × a (force = mass × acceleration). m = F ÷ a; a = F ÷ m. Units: N, kg, m/s².
Example
m = 10 kg, a = 2 m/s² → F = 20 N.
Problem 1: a car accelerating from 0 to 100 km/h
A car with a mass of 1200 kg accelerates from rest to 100 km/h in 10 seconds. What is the accelerating force, ignoring resistance?
Step 1: convert the speed to SI units. 100 km/h ÷ 3.6 = 27.78 m/s. Step 2: find the acceleration a = Δv ÷ t = 27.78 ÷ 10 = 2.778 m/s². Step 3: enter m = 1200 kg and a = 2.7778 m/s² in the calculator; the result is F ≈ 3333 N, or about 3.3 kN.
Note: entering 2.7778 makes the calculator show 3333.36 N, while the exact value is 3333.33 N. The gap comes from rounding the acceleration. Three or four significant figures are enough in the answer, so 'about 3330 N' is correct.
Problem 2: gravity, or weight in newtons
The force of gravity is a special case of Newton's second law where the acceleration is the free-fall acceleration g. At the Earth's surface g is about 9.81 m/s². A 60 kg person experiences a gravitational force of 60 × 9.81 = 588.6 N, and a 0.5 kg book 4.905 N.
Many textbooks round g to 9.8 or even 10 m/s². The 60 kg person then weighs 588 N or 600 N respectively. Use the value your teacher or textbook specifies, otherwise your answer will not match the answer key.
Problem 3: net force and friction
A 60 kg crate is pushed horizontally with a force of 300 N, and friction is 120 N. What is the crate's acceleration? A common mistake is to enter 300 N, which would give 5 m/s².
Newton's second law applies to the net force, the sum of all forces. Opposing forces are subtracted: 300 - 120 = 180 N. Enter F = 180 N and m = 60 kg, and the acceleration is 3 m/s².
Problems for finding mass and acceleration
Finding mass: a force of 500 N gives a body an acceleration of 2.5 m/s². Choose the F, a mode and enter both values; the mass is 500 ÷ 2.5 = 200 kg.
Finding acceleration: a 0.45 kg ball receives an average force of 90 N during a kick. Choose the F, m mode; the acceleration is 90 ÷ 0.45 = 200 m/s². Such a large acceleration lasts only the fraction of a second the foot is in contact with the ball.
Braking: a 1500 kg car stops from 20 m/s in 4 seconds. The deceleration is 20 ÷ 4 = 5 m/s² and the braking force is 1500 × 5 = 7500 N, pointing against the motion. Enter the magnitudes in the calculator and state the direction in your answer yourself.
Unit mistakes that ruin the answer
F = m × a gives newtons only when mass is in kilograms and acceleration in metres per second squared. Convert all data to these units before calculating.
- Mass in grams: 500 g must be entered as 0.5 kg, otherwise the force is 1000 times too large.
- Speed in km/h: to find acceleration, first divide by 3.6 to get m/s.
- Force in kilonewtons: 2.5 kN = 2500 N.
- Mixing up speed and acceleration: m/s is speed, m/s² is acceleration. A speed cannot go straight into the formula.
- Mixing up mass and weight: in everyday speech people say 'I weigh 60 kg', but in physics 60 kg is mass, while weight, the force of gravity, is about 589 N.
- Zero as an input: if the divisor is 0, the calculator shows 0, which is not a physically correct answer.
Frequently asked questions
What is Newton's second law?+
It states that force equals mass times acceleration: F = m × a.
What units does the result use?+
Force in newtons (N), mass in kilograms (kg), acceleration in m/s². 1 N = 1 kg·m/s².