Power Calculator

Free Online Power Calculator (P = W ÷ t)

This power calculator instantly solves for power, work, or time using the fundamental formula P = W ÷ t — Power equals Work divided by Time. Enter any two known values — work and time, power and time, or work and power — in any common unit, and the calculator converts everything automatically, walks through the full step-by-step solution, and plots your numbers on a labeled Power-Work-Time triangle diagram plus a work-vs-time graph, so the entire calculation is visible at a glance.

Whether you're a physics student solving a power word problem, an engineer sizing a motor or an electrical circuit, or just curious how many watts or horsepower a task actually requires, this tool handles joules, kilojoules, calories, kilocalories, foot-pounds, and ergs for work, seconds, milliseconds, minutes, and hours for time, and watts, kilowatts, horsepower, foot-pounds/second, and megawatts for power — and always shows its complete working, not just the final number.

What Is Power? (Definition and Formula)

Power is the rate at which work is done or energy is transferred — it tells you not just how much work happens, but how quickly. Two machines can do exactly the same amount of work, but the one that finishes faster has a higher power output. Power is a scalar quantity, and it is one of the most practical measurements in physics and engineering because almost every real machine — engines, motors, light bulbs, human muscles — is rated by how much power it can deliver.

The formula for mechanical power is one of the cornerstone equations of classical mechanics:

• Power (P) = Work (W) ÷ Time (t)
• The SI unit of power is the watt (W), where 1 watt = 1 joule per second (J/s).
• Example: a motor that does 5000 J of work in 10 seconds has power = 5000 ÷ 10 = 500 W

The Alternate Power Formula: P = F × v

Because work equals force times distance (W = F × d), and velocity is distance divided by time (v = d ÷ t), the power formula can also be written directly in terms of force and velocity. This version is especially useful for motion problems — vehicles, conveyor belts, elevators — where you know the applied force and the speed of movement rather than the total work and time.

• Power (P) = Force (F) × Velocity (v)
• This comes from substituting W = F × d into P = W ÷ t, then recognizing that d ÷ t = v.
• Example: a car engine applying 2000 N of force while moving at 25 m/s delivers power = 2000 × 25 = 50,000 W (50 kW)

How to Find Work from Power and Time

If you already know the power output of a machine and how long it runs, you can rearrange the formula to solve for the total work (or energy) delivered.

• Work (W) = Power (P) × Time (t)
• Example: a 100 W device runs for 60 seconds → Work = 100 × 60 = 6000 J
• This rearrangement comes directly from multiplying both sides of P = W ÷ t by t.

How to Find Time from Work and Power

If you know the total work required and the power available to do it, you can solve for how long the task will take by rearranging the formula once more.

• Time (t) = Work (W) ÷ Power (P)
• Example: a task requiring 1500 J of work, done at 250 W → Time = 1500 ÷ 250 = 6 seconds
• This rearrangement comes from dividing both sides of W = P × t by P.

The Power–Work–Time Triangle

Just like the Speed-Distance-Time and Force-Mass-Acceleration triangles, the power formula has its own 'magic triangle' for remembering all three rearranged forms. Power sits at the top, with Work and Time on the bottom row. Cover the quantity you're solving for with your finger, and what's left shows you the formula: covering P leaves W over t (W ÷ t); covering W leaves P next to t (P × t); covering t leaves W over P (W ÷ P). This calculator's diagram builds exactly this triangle using your real numbers, plus a work-vs-time graph where the slope of the line visually represents power — a steeper line always means a higher power output for the same amount of work.

Common Power, Work, and Time Units

Power, work, and time can each be expressed in several different unit systems depending on whether you're working in SI (metric), CGS, or imperial units. This calculator supports the most common ones used in physics classes, electrical engineering, and mechanical engineering.

• Power: watts (W), kilowatts (kW), horsepower (hp), foot-pounds per second (ft·lb/s), megawatts (MW)
• Work/energy: joules (J), kilojoules (kJ), calories (cal), kilocalories (kcal), foot-pounds (ft·lb), ergs
• Time: seconds (s), milliseconds (ms), minutes (min), hours (hr)
• 1 W = 1 J/s ≈ 0.00134 hp ≈ 0.7376 ft·lb/s; 1 hp ≈ 746 W

How to Use This Power Calculator

Choose what you want to find — Power, Work, or Time — from the dropdown. Then fill in the two values you already know, picking whichever unit matches your problem (joules, kilojoules, calories, kilocalories, foot-pounds, or ergs for work; seconds, milliseconds, minutes, or hours for time; watts, kilowatts, horsepower, foot-pounds/second, or megawatts for power). The calculator instantly converts everything to a common base unit, applies P = W ÷ t, and shows the result in your chosen unit — plus automatically converted into watts, kilowatts, and horsepower for quick reference.

Scroll down for the complete step-by-step solution, which mirrors exactly how you'd solve it by hand: the formula first, then your real values substituted in with unit conversion shown explicitly, then the arithmetic worked through to the final answer.

Worked Examples

Finding power from a motor: 5000 J of work done in 10 s → Power = 5000 ÷ 10 = 500 W.

Finding power from a light bulb: 6000 J of energy used in 1 minute (60 s) → Power = 6000 ÷ 60 = 100 W.

Finding power from a climber: a 2940 J of work done climbing a wall in 3 s → Power = 2940 ÷ 3 = 980 W.

Finding work: a 100 W device running for 60 s → Work = 100 × 60 = 6000 J.

Finding time: a 1500 J task done at 250 W → Time = 1500 ÷ 250 = 6 s.

Real-World Applications of the Power Formula

The power formula appears constantly across engineering, electrical systems, sports science, and everyday appliance ratings:

• Electrical engineering — power ratings (in watts) on appliances, motors, and circuits determine energy consumption and cost over time.
• Automotive engineering — engine and electric motor power (in horsepower or kilowatts) determines a vehicle's acceleration and towing capability.
• Human performance — sports scientists measure an athlete's power output (e.g., in cycling or weightlifting) to quantify explosive strength.
• Renewable energy — solar panels, wind turbines, and generators are all rated by the power (in watts or kilowatts) they can produce.
• HVAC and industrial machinery — pumps, compressors, and fans are sized using power ratings to match the work required within a given time.

Tips for Solving Power Word Problems

Most textbook and exam word problems involving power follow a predictable pattern, and a few habits make them far easier to solve correctly:

• Identify which two quantities are given and which one is being asked for — this tells you whether to use P = W ÷ t, W = P × t, or t = W ÷ P.
• Watch for problems that give force and velocity instead of work and time — use the alternate formula P = F × v instead.
• Write down the units of every given value before doing any arithmetic, and convert everything to joules and seconds first if unsure.
• Sanity-check your final answer: a light bulb is usually tens to hundreds of watts, a household appliance is hundreds to a few thousand watts, and a car engine is tens to hundreds of kilowatts.

Frequently Asked Questions

What is the formula for power? Power = Work ÷ Time (P = W ÷ t). This is the fundamental equation for mechanical power in classical mechanics.

How do you calculate power in watts? Divide the work done in joules by the time taken in seconds. For example, 200 J of work done in 4 seconds gives power = 200 ÷ 4 = 50 W.

What is the difference between work and power? Work measures the total energy transferred by a force (measured in joules); power measures how quickly that energy is transferred (measured in watts). The same work done faster means higher power.

Can this calculator solve for work or time, not just power? Yes — switch the 'What do you want to find?' dropdown to Work or Time, and the calculator rearranges the formula automatically and solves for whichever value you need.

What is the SI unit of power? The SI unit of power is the watt (W), equal to one joule per second (J/s).

How do watts convert to horsepower? 1 horsepower (hp) is approximately equal to 746 watts, so watts can be converted to horsepower by dividing by 746 (this calculator does the conversion automatically).