Work, Power & Energy — W = F·d·cosθ, P = W/t

Work, Power & Efficiency — Quick Primer

This calculator helps you connect three ideas that show up everywhere in physics and engineering: work, power, and efficiency. Whether you are pushing a cart, lifting a box, or estimating how hard a motor is working, these numbers tell you how much energy is transferred, how fast it happens, and how effectively that energy is used. The results are shown in common units like joules and watts, so the output is easy to compare with real-world devices.

In simple terms, work is energy transferred when a force moves something through a distance. The calculator uses W = F·d·cos(θ), where θ is the angle between the force and the direction of motion. A push straight ahead means θ is 0°, so all the force counts. A sideways push (90°) does no work on the motion. If the force points opposite the motion, the work is negative, which represents energy being removed by things like friction or braking.

Average power is how quickly that work is done: P_avg = W / t. It is the same idea behind a light bulb’s watt rating or the power of a bicycle sprint. Efficiency compares useful output to what you put in. If you know the input energy, the calculator uses η = W / E_in; if you know input power, it uses η = P_avg / P_in. Values above 100% usually mean the inputs do not match the situation.

To use the calculator, enter the force, displacement, and angle to find work. Add time if you want power. If you also have input energy or input power from a fuel source, battery, or motor, you can estimate efficiency. The steps are simple and you can leave unused fields blank if you only need one result.

• Step 1: Enter force (newtons) and displacement (meters).
• Step 2: Enter the angle between force and motion if it is not straight ahead.
• Step 3: Add time (seconds) to compute average power (watts).
• Step 4: Add input energy or input power to estimate efficiency (%).

Real-world examples include estimating the work done when lifting groceries, comparing the power of different drills, checking whether a winch is strong enough, or understanding why a vehicle uses more energy uphill. It is also useful in classroom problems and lab reports when you need quick, consistent calculations for work, power, and energy.