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Power from Work Calculator

Power equals work divided by time

Solution

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How It Works

Power from work is the average rate at which energy is transferred or work is done over a time interval: P = W / t. Given the total work W (in joules) and the elapsed time t (in seconds), the result is the average power in watts (1 W = 1 J/s). This is the most general definition of mechanical power and applies whenever you know how much energy was used and how long it took.

Example Problem

An electric motor lifts a 100 kg crate 5 m straight up in 10 seconds. What is the average power output? Use g = 9.81 m/s².

  1. Compute the work against gravity: W = m·g·h = 100 × 9.81 × 5 = 4905 J.
  2. Identify the elapsed time: t = 10 s.
  3. Apply the formula: P = W / t = 4905 / 10 = 490.5 W.
  4. Convert to horsepower if needed: 490.5 / 745.7 ≈ 0.66 HP.
  5. So the motor delivers about half a kilowatt of useful lifting power on average.

P = W / t gives the average power. Instantaneous power can be higher or lower at different moments during the lift.

Key Concepts

Power is the time rate of energy transfer; it is not the same as energy itself. Energy is measured in joules; power is measured in joules per second (watts). A 100 W bulb uses 100 J of energy every second. The kilowatt-hour (1 kWh = 3.6 MJ) is an energy unit even though its name contains 'watt' — it represents 1 kW running for one hour. Doubling the work done in the same time doubles the power; doubling the time for the same work halves the power.

Applications

  • Sizing an electric motor for an elevator: the motor must deliver enough power to lift the cabin in a reasonable time.
  • Rating a battery or generator: how much energy can it deliver per second under load.
  • Calculating fitness power output: how many watts a cyclist produces during a measured time interval.
  • Designing heating systems: matching a heater's wattage to the energy needed to raise room temperature in a target time.
  • Estimating data-centre cooling loads from the total work an array of servers does per hour.

Common Mistakes

  • Confusing energy with power — 'this device uses 100 watts' means 100 J/s, not 100 J total.
  • Mixing units — using kilojoules with seconds gives the answer in kW, not W; convert to consistent SI units first.
  • Forgetting efficiency — the input electrical power is always larger than the useful mechanical output because of friction and heat losses.
  • Using instantaneous force on a moving object as 'work over time' — P = W/t is the average, not the peak.
  • Treating a kilowatt-hour as a power unit. kWh measures energy; kW measures power.

Frequently Asked Questions

How do you calculate power from work?

Divide the total work done by the elapsed time: P = W / t. Use joules and seconds for an answer in watts. A 1000 J task completed in 10 s averages 100 W.

What is the formula for average power?

P = W / t, where W is the work done in joules and t is the time taken in seconds. The result is the average power in watts (1 W = 1 J/s).

What is the difference between power and energy?

Energy is the total amount transferred (joules). Power is how fast it is transferred (joules per second, or watts). A 1 kW heater running for one hour uses 1 kWh = 3.6 MJ of energy.

How do you convert watts to horsepower?

One mechanical horsepower equals 745.7 watts. Divide watts by 745.7 to get horsepower. For example, 5000 W ÷ 745.7 ≈ 6.7 HP.

Is P = W/t the same as P = Fv?

They are equivalent when the force is constant and motion is in the direction of the force. Work equals force times displacement (W = Fd), so W/t = Fd/t = F·(d/t) = F·v. P = W/t is the more general expression.

What is a typical human power output?

A trained cyclist can sustain about 300 W for an hour and peak above 1500 W for a few seconds. Everyday activities (walking, climbing stairs) generate roughly 50-200 W of mechanical power.

Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.

Worked Examples

Mechanical Engineering

How much power does it take to lift a 100 kg crate 5 m in 10 seconds?

  • Work against gravity: W = m·g·h = 100 × 9.81 × 5 = 4905 J
  • P = W / t = 4905 / 10
  • P ≈ 490.5 W — about 0.66 horsepower.

A 600 W rated hoist motor would handle this load comfortably with margin for friction losses.

Fitness Science

What average power does a cyclist who burns 720 kJ in 30 minutes produce?

  • Convert: W = 720,000 J, t = 30 × 60 = 1800 s
  • P = W / t = 720,000 / 1800
  • P = 400 W — solid amateur-racer effort.

That 720 kJ figure is the mechanical work at the pedals; total food-calorie expenditure is ~3-4× higher because human cycling efficiency is around 22-25 %.

Home Energy

What is the average power of a 3.6 MJ space heater running for one hour?

  • Convert: W = 3,600,000 J, t = 3600 s
  • P = W / t = 3,600,000 / 3600
  • P = 1000 W = 1 kW — exactly one kilowatt-hour of energy.

This is the canonical conversion: 1 kWh = 3.6 MJ. A 1 kW heater running for one hour uses exactly 1 kWh of electricity.

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