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The Work and Power Calculator combines two fundamental physics calculations into a single tool. Work measures the total energy transferred by a force over a distance, while power measures how quickly that energy transfer occurs. Together, they provide a complete picture of mechanical performance — essential for evaluating engines, human athletic output, construction equipment, and any system where force produces motion.
This calculator takes force, displacement, angle, and time as inputs, then computes both work ($$W = Fd\cos\theta$$) and average power ($$P = W/t$$) simultaneously. The angle input allows for forces applied at any direction relative to the displacement. It also calculates the average velocity over the displacement. These combined outputs are particularly useful in biomechanics (analyzing lifting tasks), automotive engineering (evaluating drivetrain performance), and physics education (connecting the concepts of work and power in a single analysis).
The calculator chains two formulas:
Step 1 — Work: $$W = F \cdot d \cdot \cos\theta$$
where $$F$$ is force (N), $$d$$ is displacement (m), and $$\theta$$ is the angle between force and displacement direction.
Step 2 — Power: $$P = \frac{W}{t}$$
where $$t$$ is the time (s) taken to perform the work. Average velocity is $$v_{avg} = d/t$$, which connects to the alternative power formula $$P = F \cdot v \cdot \cos\theta$$. Results appear in joules, kilojoules, watts, and horsepower.
The work value represents total energy transferred. The power value indicates the rate of energy transfer — a more powerful system completes the same work faster. For example, two cranes lifting identical loads to the same height do equal work, but the faster crane delivers more power. The average velocity output helps verify consistency with the force-velocity power formula.
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Results
Pushing with 80 N at 25° over 20 m in 10 s: W = 80×20×cos(25°) ≈ 1450 J, P ≈ 145 W (0.19 hp).
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Results
A 5000 N pull over 100 m in 30 s: W = 500 kJ, P = 16.67 kW (22.4 hp) at 3.33 m/s average speed.
Work tells you the total energy cost of a task, while power tells you the rate requirement. A motor might have enough energy (work capacity) but insufficient power to complete a task in the required time. Evaluating both ensures a system meets both energy and time constraints.
When $$\theta = 90°$$, $$\cos 90° = 0$$, so both work and power are zero. The force is entirely perpendicular to the motion and transfers no energy. An example is carrying a box horizontally — gravity acts downward but motion is horizontal.
This calculator computes average power ($$P = W/t$$). Instantaneous power may vary if force or velocity change during the motion. For constant force and velocity, average and instantaneous power are equal.
Efficiency is the ratio of useful output work to total input work. If this calculator gives the input work and you know the useful output, efficiency = (output work / input work) × 100%. Power efficiency works the same way: $$\eta = P_{out}/P_{in}$$.
Yes. For vertical lifting at constant speed, the force equals weight ($$F = mg$$), the distance is the height lifted, the angle is 0° (force and displacement both upward), and $$W = mgh$$. Power then gives you the lifting rate.
Work: joules (J), kilojoules (kJ), kilowatt-hours (kWh), foot-pounds (ft·lb), calories (cal). Power: watts (W), kilowatts (kW), horsepower (hp), BTU/hour. This calculator provides SI units plus horsepower.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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