Power Calculator
Calculate power, work, or time using the power formula: P = W / t
Step-by-Step Solution:
1. Using the power formula: P = W / t
2. Substitute the values:
P = 1000 J / 5 s
3. Calculate:
P = 200 J/s (watts)
What is Power?
Power is the rate at which work is done or energy is transferred over time. It tells you not just how much energy is used, but how quickly it is used. A powerful engine doesn't necessarily do more work — it does the same work in less time.
Power Formula:
P = W / t
where: - P = power (measured in watts) - W = work done or energy transferred (measured in joules) - t = time taken (measured in seconds)
This formula can be rearranged to solve for any variable: - Work: W = P × t - Time: t = W / P
How to Calculate Power
To find power, follow these steps:
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Determine the work done: Calculate or measure the total work or energy transferred (in joules)
-
Measure the time taken: Record how long it took to do the work (in seconds, minutes, or hours)
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Divide work by time: Use the formula P = W / t
-
Include units: Express your answer in watts (W), kilowatts (kW), or other power units
Example: A crane lifts a load, doing 5000 joules of work in 10 seconds. - P = 5000 J / 10 s = 500 W
Understanding Power and Watts
The watt is named after James Watt, the Scottish inventor who improved the steam engine. One watt equals one joule per second — it represents a continuous rate of energy transfer.
Common power scales: - 1 W — a small LED light - 60 W — a traditional incandescent light bulb - 746 W — one horsepower - 1,000 W (1 kW) — a small space heater - 100,000 W (100 kW) — a typical car engine - 1,000,000 W (1 MW) — a small wind turbine
Power in Different Contexts
Mechanical Power: P = F × v (force times velocity), useful when an object moves at constant speed under a force.
Electrical Power: P = V × I (voltage times current), used in circuit analysis.
Rotational Power: P = τ × ω (torque times angular velocity), used for motors and engines.
Real-World Applications of Power
- Electrical engineering: Sizing circuits, generators, and motors
- Automotive: Rating engine output in horsepower or kilowatts
- Home energy: Understanding appliance wattage and electricity costs
- Exercise science: Measuring athletic performance in watts (cycling, weightlifting)
- HVAC systems: Sizing heating and cooling equipment
- Renewable energy: Rating solar panels and wind turbines
Common Questions About Power
What is the formula for power?
The power formula is P = W / t, where P is power, W is work done, and t is time taken. Power measures how quickly work is performed or energy is transferred.
What is the unit of power?
The SI unit of power is the watt (W), which equals one joule per second (J/s). Other common units include kilowatts (kW), horsepower (hp), and foot-pounds per second.
What is the difference between work and power?
Work measures the total energy transferred (W = F × d), while power measures the rate at which work is done (P = W / t). Two people can do the same amount of work, but the one who finishes faster exerts more power.
How do you convert watts to horsepower?
To convert watts to horsepower, divide by 745.7. For example, 1000 watts = 1000 / 745.7 ≈ 1.34 horsepower. One mechanical horsepower equals approximately 745.7 watts.