Energy Calculator KE & GPE
Calculate kinetic energy, gravitational PE, work done, elastic PE, and power with step-by-step solutions. Perfect for GCSE and A-Level Physics.
Kinetic Energy = ½ × Mass × Velocity²
Solve for:
Quick Examples
Work Done
Work equals force times distance
Kinetic Energy
Energy of moving objects
Gravitational PE
Energy due to height
Elastic PE
Energy in stretched springs
Efficiency
Useful energy as percentage
Power
Rate of energy transfer
What is Energy?
Energy is the capacity to do work. It is one of the most fundamental concepts in physics. Energy is measured in Joules (J), named after the English physicist James Prescott Joule.
Types of Energy
- • Kinetic - energy of moving objects
- • Gravitational PE - energy due to height
- • Elastic PE - energy in stretched springs
- • Thermal - energy from heat
- • Chemical - energy stored in bonds
- • Electrical - energy from charges
- • Nuclear - energy from atomic nuclei
Conservation of Energy
The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed from one form to another.
In a closed system, the total energy remains constant. For example, when a ball falls, its GPE converts to KE, but the total energy stays the same.
Kinetic Energy (KE = ½mv²)
Kinetic energy is the energy an object has due to its motion. Any moving object has kinetic energy - from a speeding car to a flying football.
KE = ½mv²
KE = kinetic energy (J) | m = mass (kg) | v = velocity (m/s)
⚠️ Important: Velocity is Squared!
Because velocity is squared in the formula, doubling velocity quadruples kinetic energy. This is why car stopping distances increase dramatically at higher speeds, and why car crashes are so much more dangerous at high speeds.
Gravitational Potential Energy (GPE = mgh)
Gravitational potential energy is the energy an object has due to its position in a gravitational field. The higher an object is lifted, the more GPE it gains.
GPE = mgh
GPE = gravitational PE (J) | m = mass (kg) | g = gravity (m/s²) | h = height (m)
🌍
Earth
g = 9.81 m/s²
🌙
Moon
g = 1.62 m/s²
🔴
Mars
g = 3.71 m/s²
Work Done (W = Fd)
Work is done when a force causes an object to move. Work done equals energy transferred - this is a key concept linking forces and energy.
W = Fd
For force parallel to motion
W = Fd cos θ
For force at angle θ to motion
Note: If force is perpendicular to motion (θ = 90°), no work is done because cos(90°) = 0. This is why carrying a heavy bag horizontally doesn't do work on the bag - the force is vertical but motion is horizontal.
Power (P = E/t)
Power is the rate of energy transfer. It tells us how quickly energy is being used or transferred. Power is measured in Watts (W).
P = E/t
Power = Energy ÷ Time
P = Fv
For constant velocity motion
1 Watt = 1 Joule per second. A 100W light bulb transfers 100 joules of energy every second. The P = Fv formula is useful for calculating the power needed to move at constant velocity against a resistive force.
Efficiency
No machine is 100% efficient. Some energy is always "lost" (converted to less useful forms like heat). Efficiency tells us what percentage of input energy becomes useful output.
Efficiency = (Useful Output ÷ Total Input) × 100%
90%
LED bulb
5%
Incandescent bulb
25%
Petrol engine
90%
Electric motor
Common Mistakes to Avoid
Forgetting to square velocity in KE formula
✓ KE = ½mv², not ½mv
Using wrong units
✓ Always use SI units: kg, m, s, J, W
Confusing energy and power
✓ Energy is total (J), power is rate (W = J/s)
Thinking efficiency can exceed 100%
✓ Impossible - output ≤ input always
Forgetting angle for work done
✓ Use W = Fd cos θ for angled forces
Mixing up GPE reference points
✓ Only changes in height matter
Worked Examples
A car of mass 1500 kg is travelling at 20 m/s. Calculate its kinetic energy.
KE = ½mv² = ½ × 1500 × 20²
KE = ½ × 1500 × 400 = 300,000 J = 300 kJ
A 2 kg ball is dropped from 5 m. What is its speed just before hitting the ground? (g = 10 m/s²)
GPE lost = KE gained
mgh = ½mv² → gh = ½v² → v = √(2gh)
v = √(2 × 10 × 5) = √100 = 10 m/s
A spring with k = 200 N/m is stretched by 0.1 m. How much energy is stored?
EPE = ½kx² = ½ × 200 × (0.1)²
EPE = ½ × 200 × 0.01 = 1 J
A motor uses 500 J of electrical energy and does 375 J of useful work. What is its efficiency?
Efficiency = (Output ÷ Input) × 100%
Efficiency = (375 ÷ 500) × 100% = 75%
A crane lifts a 200 kg load through 15 m in 30 seconds. Calculate the power of the crane. (g = 10 m/s²)
Work done = GPE gained = mgh = 200 × 10 × 15 = 30,000 J
Power = Work ÷ Time = 30,000 ÷ 30 = 1000 W = 1 kW
Frequently Asked Questions
What is the unit of energy?
The SI unit of energy is the Joule (J). 1 J = 1 N·m = 1 kg·m²/s².
Why does KE depend on v²?
Because the work needed to accelerate increases with speed. More force is needed over the same distance at higher speeds.
Can GPE be negative?
Yes! GPE depends on your reference point. Below the reference level, GPE is negative.
What does 1 Watt mean?
1 Watt = 1 Joule per second. It measures how fast energy is transferred.
Is work done a vector?
No, work is a scalar quantity. It has magnitude but no direction.
Why isn't anything 100% efficient?
Friction and other losses always convert some energy to heat, which is usually not useful.
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