Work, potential energy and kinetic energy are three sides of the same physical coin – all measured in joules. Whether you want to calculate how much energy a falling rock releases on impact, how much work a crane does lifting a component, or how much kinetic energy a vehicle dissipates during braking – the work and energy calculator covers all three cases.
Step by Step: How to Use the Work and Energy Calculator
- Choose the calculation type: Select from mechanical work (W = F × s), potential energy (Ep = m × g × h) or kinetic energy (Ek = ½ × m × v²).
- Set the units: Force in Newtons (N), distance in metres (m), mass in kg, height in m, velocity in m/s. Result in joules (J) or kilowatt-hours (kWh).
- Enter the known values: Fill in the known quantities. The calculator computes the unknown and shows all intermediate steps.
- Convert energy units: 1 kWh = 3,600,000 J. For practical energy comparisons, the calculator displays results in both joules and kWh.
- Calculate power: If you know the time duration, the calculator also works out power: P = W/t in watts.
Practical Examples
Example 1 – Crane lifting a steel beam: Mass 2,500 kg, lifting height 12 m. Potential energy: Ep = 2,500 × 9.81 × 12 = 294,300 J = 294.3 kJ. If the crane lifts in 90 seconds: Power P = 294,300 / 90 = 3,270 W = 3.27 kW. This determines the minimum motor power required.
Example 2 – Braking energy of a car: Vehicle mass 1,600 kg, speed 90 km/h = 25 m/s. Kinetic energy: Ek = ½ × 1,600 × 25² = 800 × 625 = 500,000 J = 500 kJ. During a full brake application this energy is converted entirely into heat – spread across four brake discs. Regenerative braking in an electric vehicle can recover up to 70% of this energy.
Example 3 – Mountain hike: Hiker (85 kg including backpack) climbs 650 metres of altitude. Potential energy: 85 × 9.81 × 650 = 542,317.5 J = 542.3 kJ ≈ 130 kcal. This is the pure lifting work component – the actual calorie expenditure is about four times higher (≈ 520 kcal) due to the human body's roughly 25% mechanical efficiency.
Work and Energy Formulas
Mechanical work: W = F × s (joules). Potential energy: Ep = m × g × h. Kinetic energy: Ek = ½ × m × v². 1 kWh = 3,600,000 J = 3.6 MJ. 1 horsepower = 745.7 watts.
Frequently Asked Questions (FAQ)
What is the difference between work and energy?
Energy is the stored capacity to do work. Work is the process by which energy is transferred or converted. When a weight falls, it converts potential energy into kinetic energy – the work done equals the change in energy. Both are measured in joules.
Why is kinetic energy proportional to the square of velocity?
At double the speed, kinetic energy is four times as large. This has serious consequences in road traffic: a vehicle at 100 km/h has four times the impact energy compared to 50 km/h. This is the physical reason why speed limits in residential areas matter so much for crash severity.
How many joules are in one kilowatt-hour?
1 kWh = 1,000 W × 3,600 s = 3,600,000 J = 3.6 MJ. For comparison: one litre of petrol contains approximately 34,000 kJ = 9.4 kWh of chemical energy. With a petrol engine efficiency of around 30–40%, a maximum of about 3.5 kWh of mechanical energy is extracted from 9.4 kWh of fuel.
