Instantaneous Power Calculator

Calculator

Choose a model, enter values, and compute power at that instant. Use signed values when direction matters.

• Mechanical: P = F · v (colinear force and velocity).
• Rotational: P = τ · ω (torque times angular speed).
• Electrical: p(t) = v(t) i(t) (instantaneous voltage and current).
• Energy rate: P ≈ ΔW / Δt over a short interval.

Units: power in watts (W). Positive values indicate energy delivery. Negative values indicate energy return, such as braking or regeneration.

1. Select the calculation mode that matches your situation.
2. Enter the required values and choose their units.
3. Set the desired decimal precision for displayed results.
4. Click Calculate Instantaneous Power to view results above.
5. Use the CSV or PDF buttons to download your result.

1) What instantaneous power means

Instantaneous power describes how fast energy transfers at a specific moment. In mechanics it is the time rate of doing work, and in circuits it is the product of voltage and current at that same instant. The unit is the watt (1 W = 1 J/s).

2) Mechanical data and typical ranges

For straight‑line motion with aligned force and velocity, power is P = F·v. Example: 120 N pushing at 3.5 m/s gives 420 W. Human cycling output is often 100–300 W steady, while short sprints may exceed 800 W.

3) Rotational machines and RPM conversion

Rotating systems use P = τ·ω. The calculator converts rpm to rad/s using ω = 2π·rpm/60. Example: 45 N·m at 1200 rpm produces about 5.65 kW, typical of small industrial drives or workshop tools.

4) Electrical instantaneous power

Electrical power is p(t) = v(t)i(t). With 230 V and 6.2 A, power is 1426 W. For AC, instantaneous power can change each cycle; use consistent inputs (instantaneous samples or RMS with the correct power factor when needed).

5) Using ΔW/Δt for short intervals

If you know an energy change over a brief period, estimate power using P ≈ ΔW/Δt. For 1.8 kJ delivered in 3 s, power is 600 W. This approach is common for pulsed heating, bursts in actuators, and short test runs.

6) Sign, direction, and regeneration

Power can be positive or negative depending on your sign convention. Negative values often indicate energy flowing back, such as regenerative braking in vehicles or a generator absorbing torque. Use signed velocity, torque, voltage, or current to represent direction correctly.

7) Unit handling and precision

This tool converts force (N, kN, lbf), speed (m/s, km/h, ft/s), torque (N·m, kN·m, lbf·ft), and angular speed (rad/s, rpm) into SI before computing. Precision controls the displayed digits in W, kW, and horsepower (hp).

8) Practical checks and reporting

Validate results by comparing against rated equipment values. For example, 1 hp is about 746 W, so 5.65 kW is roughly 7.6 hp. Use the export buttons to keep a record of inputs, SI conversions, and computed power for labs, maintenance logs, or design notes.

1) What is the difference between power and energy?

Energy is the total amount transferred or stored, measured in joules. Power is the rate of energy transfer, measured in watts, and can vary moment to moment.

2) When should I use mechanical vs rotational mode?

Use mechanical mode for straight motion with a force along the direction of travel. Use rotational mode for shafts, motors, and gears where torque and angular speed define the output.

3) How do I handle non‑colinear force and velocity?

Compute the effective force component along motion using F·cos(θ), then enter that force with the speed. This yields the correct instantaneous power along the path.

4) Does the electrical mode work for AC circuits?

Yes, if your inputs match your intent. Use instantaneous samples for true instantaneous power. If using RMS values, include power factor externally and interpret the result as real power only when consistent.

5) Why can power be negative?

Negative power indicates energy is flowing opposite your chosen positive direction, such as a braking force, a generator absorbing mechanical input, or a load returning energy to the source.

6) What does horsepower mean here?

The calculator reports mechanical horsepower using 1 hp ≈ 745.7 W. It is a convenient comparison unit for motors and engines, alongside watts and kilowatts.

7) What is a quick sanity check for results?

Convert watts to kilowatts and compare to typical device ratings. Also check units: doubling force or velocity doubles mechanical power, and doubling torque or rpm doubles rotational power.