Energy Calculations GCSE: Formulas & Examples

This guide explains the energy calculations you need for GCSE Physics: kinetic energy, gravitational potential energy, elastic potential energy, and the principle of conservation of energy. You’ll learn the formulas, how to apply them, and how to avoid common mistakes.

What Is Energy in GCSE Physics?

Energy is a measure of a system’s ability to do work or cause change. In GCSE physics, energy is measured in joules (J). The key idea is that energy cannot be created or destroyed, only transferred from one store to another. This is called the principle of conservation of energy. For calculations, you focus on the amount of energy in different stores, such as kinetic (movement), gravitational potential (height), and elastic potential (stretched or compressed materials).

Kinetic Energy Formula

Kinetic energy (KE) is the energy an object has because it is moving. The formula is:

KE = ½ × mass × speed²

• KE = kinetic energy in joules (J)
• mass (m) = mass of the object in kilograms (kg)
• speed (v) = speed of the object in metres per second (m/s)

Notice that speed is squared. This means if you double the speed, the kinetic energy becomes four times larger. For example, a car at 20 m/s has four times the kinetic energy of the same car at 10 m/s.

Gravitational Potential Energy Formula

Gravitational potential energy (GPE) is the energy stored in an object due to its height above the ground. The formula is:

GPE = mass × gravitational field strength × height

• GPE = gravitational potential energy in joules (J)
• mass (m) = mass in kilograms (kg)
• gravitational field strength (g) = in newtons per kilogram (N/kg). On Earth this is approximately 9.8 N/kg, but many GCSE exams use 10 N/kg to simplify calculations.
• height (h) = height above the reference point in metres (m)

For example, a 2 kg object lifted 3 m on Earth (using g = 10 N/kg) gains GPE = 2 × 10 × 3 = 60 J.

Elastic Potential Energy Formula

Elastic potential energy (EPE) is stored when an object is stretched or compressed, like a spring or rubber band. The formula is:

EPE = ½ × spring constant × extension²

• EPE = elastic potential energy in joules (J)
• spring constant (k) = in newtons per metre (N/m)
• extension (e) = how much the spring has been stretched or compressed from its natural length, in metres (m)

This is similar in shape to the kinetic energy formula because both involve a squared term. The spring constant measures how stiff the spring is – a higher k means a stiffer spring that stores more energy for the same extension.

Worked Example: Using the Calculator

Let’s use the kinetic energy calculator above with the default values: mass = 10 kg, speed = 5 m/s.

1. Write down the formula: KE = ½ × m × v²
2. Substitute the values: KE = ½ × 10 × (5)²
3. Calculate the square: (5)² = 25
4. Multiply: ½ × 10 × 25 = 5 × 25 = 125 J

The calculator gives 125.00 J, which matches. Notice the units: kg × (m/s)² = kg·m²/s² = J (joule).

Conservation of Energy in Calculations

Many GCSE problems involve energy transfers between stores. For example, a ball dropped from a height converts gravitational potential energy into kinetic energy as it falls. Ignoring air resistance, the GPE at the top equals the KE just before it hits the ground. This lets you find the speed of the ball: set GPE = KE, then solve for speed.

Example: A 0.5 kg ball is dropped from a height of 2 m (g = 10 N/kg). GPE = 0.5 × 10 × 2 = 10 J. At the ground, KE = 10 J. Using KE = ½ × m × v², you get 10 = ½ × 0.5 × v², so v² = 40, and v ≈ 6.32 m/s. In reality, air resistance reduces the speed, so the actual value would be slightly lower.

Common Mistakes and How to Avoid Them

• Forgetting to square the speed or extension – this is the most frequent error. Always apply the square to the whole value, not just the number.
• Using the wrong units – mass must be in kg, speed in m/s, height in m. If a question gives grams or km, convert first.
• Mixing up gravitational field strength (g) with acceleration due to gravity – they are numerically equal on Earth, but g is a field strength in N/kg, not an acceleration.
• Not converting extension to metres – if a spring stretches 5 cm, that’s 0.05 m, not 5 m.
• Rounding too early – keep full values until the final step to avoid rounding errors.

Limits of the Formulas

These formulas are idealised. Kinetic energy assumes no air resistance. Gravitational potential energy assumes a constant gravitational field strength, which is fine near Earth’s surface but not in space. Elastic potential energy follows Hooke’s law only up to the limit of proportionality – beyond that, the spring may be permanently deformed. In your exams, these simplifications are expected, but you should mention them when explaining real-world results.

Frequently Asked Questions

What does the ‘½’ in kinetic energy mean?
The ½ comes from calculus – it’s the result of integrating force over distance. In practice, it makes the formula work correctly: for a constant force, the work done equals ½ × mass × velocity². You don’t need to derive it for GCSE, just use it.

Why is speed squared in kinetic energy?
Because kinetic energy depends on both the force and the distance over which it acts. When you double the speed, the object has twice the momentum, and it also travels twice as far while decelerating to a stop, so the work done (and energy) is four times greater.

Can I use the same formula for elastic potential energy for any stretch?
No. The formula EPE = ½ke² only works if the spring obeys Hooke’s law, meaning the force is proportional to extension. If you stretch a spring too far, it may reach its elastic limit and not return to its original shape.

What is the difference between kinetic and potential energy?
Kinetic energy is energy of motion – any moving object has it. Potential energy is stored energy due to position or configuration – gravitational potential energy depends on height, elastic potential energy depends on deformation. They can convert into each other, but total energy is conserved.

How do I choose which formula to use in a question?
Look for keywords: “moving� or “speed� suggests kinetic energy; “height� or “lifted� suggests gravitational potential; “spring�, “stretched� or “compressed� suggests elastic potential. If a question describes a transfer, write down both formulas and set them equal.

What if the question gives power instead of energy?
Power is the rate of energy transfer, measured in watts (W) or joules per second. To find energy, multiply power by time: Energy (J) = Power (W) × time (s). This is separate from the energy store formulas, but often appears in the same topic.

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in m | Mass | kg | 10 | 0
in v | Speed | m/s | 5 | 0
out ke | Kinetic energy | J | 0.5 * m * v^2 | 2