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Free Force Calculator (F = m·a)

This force calculator applies Newton's second law of motion, F = m·a, to relate force (F), mass (m), and acceleration (a). Enter any two of the three quantities and the calculator solves for the missing one, returning force in newtons (N), mass in kilograms (kg), or acceleration in metres per second squared (m/s²). Newton's second law is the cornerstone of classical mechanics: it tells you that the net force on an object equals its mass multiplied by the acceleration that force produces, which is exactly what you need when analysing pushes, pulls, weight, friction, or any everyday motion problem.

Enter any two values — the third is calculated from F = m·a.

Results
Force98 N
Mass10 kg
Acceleration9.8 m/s²

F = m · a — m = F / a — a = F / m. Uses SI units: newtons (N), kilograms (kg) and m/s². For weight, set a = g ≈ 9.8 m/s².

Quick answer

Newton's second law states that force equals mass times acceleration: F = m·a. Force (F) is measured in newtons (N), mass (m) in kilograms (kg), and acceleration (a) in metres per second squared (m/s²). To find a missing quantity, rearrange the formula: mass is m = F / a and acceleration is a = F / m.

Formula & method

F = m · a    •    m = F / a    •    a = F / m
  • F — Net force in newtons (N)
  • m — Mass in kilograms (kg)
  • a — Acceleration in metres per second squared (m/s²)

F = net force (newtons, N), m = mass (kilograms, kg), a = acceleration (metres per second squared, m/s²). One newton is the force that accelerates a 1 kg mass at 1 m/s². To find an object's weight, use a = g ≈ 9.8 m/s² (standard gravity 9.80665 m/s²).

Examples

Example 1: Weight of a 10 kg mass under gravity
Input
m = 10 kg, a = 9.8 m/s²
Result
F = 98 N
Why
With mass and acceleration known, apply F = m·a = 10 × 9.8 = 98 newtons. Because the acceleration here is standard gravity (g ≈ 9.8 m/s²), this 98 N is the object's weight — the downward gravitational force on a 10 kg mass.
Example 2: Acceleration of a car from engine force
Input
F = 2000 N, m = 500 kg
Result
a = 4 m/s²
Why
Rearranging F = m·a gives a = F / m = 2000 / 500 = 4 m/s². A net forward force of 2000 N on a 500 kg vehicle produces an acceleration of 4 metres per second squared, meaning its speed increases by 4 m/s every second.
Example 3: Mass from a known force and acceleration
Input
F = 147 N, a = 9.8 m/s²
Result
m = 15 kg
Why
Rearranging F = m·a gives m = F / a = 147 / 9.8 = 15 kilograms. Since the acceleration is g ≈ 9.8 m/s², this works backwards from a measured weight of 147 N to find that the object has a mass of 15 kg.
Example 4: Force to push a loaded cart
Input
m = 1200 kg, a = 3 m/s²
Result
F = 3600 N
Why
Apply F = m·a = 1200 × 3 = 3600 newtons. To accelerate a 1200 kg cart at 3 m/s², the net (unbalanced) force must be 3600 N; any friction or drag would have to be added on top of this to find the total applied force.

When to use this tool

  • Calculating the weight (in newtons) of an object from its mass, using acceleration due to gravity, g ≈ 9.8 m/s².
  • Finding the acceleration a vehicle, cart, or object will undergo when a known net force is applied to a known mass.
  • Working out how much force is needed to accelerate a given mass at a target rate, for example in a physics homework problem or an engineering estimate.
  • Checking the answer to a Newton's second law problem and seeing the rearranged formula and steps, rather than only the final number.
  • Teaching or learning the fundamental relationship between force, mass, and acceleration in introductory mechanics.

Common mistakes

  • Confusing mass with weight. Mass (in kilograms) measures the amount of matter and stays the same everywhere, while weight is a force (in newtons) equal to m × g. A 10 kg object always has 10 kg of mass but weighs about 98 N on Earth and far less on the Moon.
  • Forgetting that F is the net (resultant) force. F = m·a uses the vector sum of all forces acting on the object. If friction, drag, or an opposing push is present, subtract those before using the result, or you will overestimate the acceleration.
  • Using inconsistent units. The formula gives newtons only when mass is in kilograms and acceleration is in m/s². Mixing in grams, pounds, or cm/s² without converting first produces wrong answers — convert grams to kilograms by dividing by 1000.
  • Dividing by zero. Acceleration a = F / m is undefined when mass is zero, and mass m = F / a is undefined when acceleration is zero. A non-zero net force with zero acceleration is physically impossible for a real (non-zero) mass.
  • Treating g as exactly 10 or exactly 9.81 everywhere. Standard gravity is 9.80665 m/s², but the local value varies slightly with latitude and altitude, so weight calculations carry a small uncertainty.

Frequently asked questions

What is the formula for force?

The formula for force is Newton's second law, F = m·a, where F is the net force in newtons (N), m is the mass in kilograms (kg), and a is the acceleration in metres per second squared (m/s²). It says that the net force on an object equals its mass multiplied by the acceleration that force produces. Rearranged, mass is m = F / a and acceleration is a = F / m.

What is one newton in everyday terms?

One newton (N) is defined as the force that gives a mass of one kilogram an acceleration of one metre per second squared (1 N = 1 kg·m/s²). As a rough feel, one newton is about the weight of a small apple (roughly 100 grams) held in your hand on Earth, since 0.1 kg × 9.8 m/s² ≈ 1 N.

How do I calculate weight from mass?

Weight is a force, so you use F = m·a with the acceleration set to gravity, g. On Earth, g ≈ 9.8 m/s² (more precisely 9.80665 m/s²), so a 10 kg mass weighs about 10 × 9.8 = 98 N. To convert weight back to mass, divide the force by g: m = F / g.

What is the difference between mass and force?

Mass measures how much matter an object contains and is the same everywhere; it is measured in kilograms. Force is a push or pull that can change motion and is measured in newtons. They are linked by F = m·a: the same force produces less acceleration on a larger mass, and weight is simply the force of gravity acting on a mass.

Does this calculator account for friction or air resistance?

No. The calculator uses the net force, meaning the single resultant of all forces acting on the object. If friction, drag, or another opposing force is present, you must subtract it yourself to get the net force before reading off the acceleration, or add it to the result when finding the force you need to apply.

What units does the force calculator use?

It uses SI base units: mass in kilograms (kg), acceleration in metres per second squared (m/s²), and force in newtons (N). If your data is in other units — grams, pounds, or cm/s² — convert to kilograms and m/s² first so the result comes out correctly in newtons.

Can I use F = m·a for objects in space or on the Moon?

Yes. Newton's second law F = m·a holds anywhere, because mass does not change with location. What changes is the acceleration: gravity on the Moon is about 1.62 m/s² instead of Earth's 9.8 m/s², so the same mass weighs roughly one sixth as much, even though its mass in kilograms is identical.

Sources & references

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