How to Calculate Force in Physics (With Examples)

What Is Force?

A force is a push or pull that can change an object's motion. Forces can:

• Make objects start moving
• Make objects speed up or slow down
• Change an object's direction
• Deform (change the shape of) an object

Force is a vector quantity — it has both magnitude (size) and direction. The standard unit of force is the Newton (N).

Newton's Second Law: F = ma

The most important formula for force calculations is Newton's second law of motion:

F = m × a

Where:

• F = force (in Newtons, N)
• m = mass (in kilograms, kg)
• a = acceleration (in meters per second squared, m/s²)

This formula tells us that force equals mass times acceleration. It can be rearranged:

• a = F / m (to find acceleration)
• m = F / a (to find mass)

For more on Newton's laws, see our guide on Newton's Laws of Motion.

Step-by-Step Examples

Example 1: Finding force

A 10 kg box is pushed with an acceleration of 3 m/s². What force is applied?

F = m × a = 10 × 3 = 30 N

Example 2: Finding acceleration

A 50 N force acts on a 5 kg object. What is the acceleration?

a = F / m = 50 / 5 = 10 m/s²

Example 3: Finding mass

A force of 200 N produces an acceleration of 4 m/s². What is the mass?

m = F / a = 200 / 4 = 50 kg

Example 4: Force with deceleration

A car with mass 1200 kg brakes and decelerates at 5 m/s². What is the braking force?

F = m × a = 1200 × 5 = 6000 N (in the opposite direction of motion)

Calculating Weight

Weight is the force of gravity pulling on an object. It's calculated using:

W = m × g

Where:

• W = weight (in Newtons)
• m = mass (in kg)
• g = acceleration due to gravity ≈ 9.8 m/s² on Earth

Examples:

Your weight: If you have a mass of 60 kg: W = 60 × 9.8 = 588 N

An apple (0.1 kg): W = 0.1 × 9.8 = 0.98 N ≈ 1 N

Weight vs Mass

| | Mass | Weight | |---|---|---| | What is it? | Amount of matter | Force of gravity | | Unit | kg | N (Newtons) | | Changes with location? | No | Yes (different on Moon vs Earth) | | On the Moon | Same | About 1/6 of Earth weight |

For more on this, see mass vs weight explained.

Net Force

When multiple forces act on an object, the net force (or resultant force) is the combination of all forces.

Same direction

If two people push a box in the same direction with 20 N and 15 N:

Net force = 20 + 15 = 35 N (in that direction)

Opposite directions

If one person pushes with 30 N to the right and another pushes with 10 N to the left:

Net force = 30 − 10 = 20 N (to the right)

Balanced forces

If forces are equal and opposite, the net force is zero and the object stays at rest (or keeps moving at constant velocity).

Example: A book on a table has gravity (weight) pulling it down and the table pushing it up (normal force). These forces balance, so the book doesn't accelerate.

Friction Force

Friction is a force that opposes motion. It acts in the opposite direction to movement.

Friction = μ × N

Where:

• μ (mu) = coefficient of friction (depends on the surfaces)
• N = normal force (usually equals weight on a flat surface)

Example:

A 20 kg box is pushed across a floor with μ = 0.3. What is the friction force?

Normal force = weight = 20 × 9.8 = 196 N Friction = 0.3 × 196 = 58.8 N

To accelerate the box, you need to push with more than 58.8 N.

Units of Force

| Quantity | Unit | Symbol | |---|---|---| | Force | Newton | N | | Mass | Kilogram | kg | | Acceleration | Meters per second squared | m/s² |

1 Newton is the force needed to accelerate a 1 kg mass at 1 m/s².

Other force units you might encounter:

• kilonewton (kN) = 1000 N (for large forces)
• dyne = 10⁻⁵ N (CGS system)
• pound-force (lbf) ≈ 4.448 N (imperial system)

Practice Problems

1. Find the force needed to accelerate a 15 kg object at 4 m/s².
2. What acceleration does a 100 N force give to a 25 kg object?
3. What is the weight of a 75 kg person on Earth?
4. Two forces act on an object: 50 N right and 30 N left. What is the net force?
5. A 10 kg box has μ = 0.4 on a floor. What force is needed to start it sliding?

Answers: (1) 60 N (2) 4 m/s² (3) 735 N (4) 20 N right (5) 39.2 N

Need More Help?

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