Power Calculator
The pace of the ledger: energy delivered per second, in watts and in the horsepower Watt priced from draft horses — derived here from exact definitions, not quoted from a sticker.
Power Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Average power over the interval — no peak/continuous rating distinction
- Mechanical horsepower definition; electrical 746 W named but not used
In short: 5,000 J delivered in 10 s is P = 5,000/10 = 500 W — 0.670511 of the mechanical horsepower Watt standardised at 550 foot-pounds per second. Sustained for an hour, that pace moves 1,800,000 J = 0.5 kWh: the same 5,000 J banked in 1 s would be 5,000 W, ten times the pace for the same amount. That is the whole idea — work is the amount, power is the rate, and halving the time doubles the bill per second without moving the ledger's total. Engines compete on this page; banks of batteries compete on the other one.
Formula
P = W/t · 1 hp = 550 ft·lbf/s = 550 × 0.45359237 × 9.80665 × 0.3048 W · 1 kWh = 1,000 W × 3,600 s
Watt's horsepower was a marketing number that became a standard: 550 foot-pounds of lifting per second. With the pound (0.45359237 kg), standard gravity (9.80665 m/s²) and the foot (0.3048 m) all exact, that is 745.699871582270 watts — derived on this page from definitions, not copied from a rounding. The electric 746 W is a DIFFERENT convention, rounded for switchgear; the pages keep the mechanical one.
Worked Example
- Enter the energy delivered and the time it took.
- Read watts for the pace; horsepower for the showroom.
- Use the hour card to translate pace into billable energy — kWh is what the meter sells.
- Compare two machines on the SAME energy before praising the faster one.
Defaults: 5,000 J over 10 s → 500 W = 0.670511 hp. Same energy in 1 s → 5,000 W; in an hour → 0.5 kWh. The total never moved — only the pace.
Strengths & Limits Of This Model
Where this engine is strong
- hp derived from exact definitions on the page
- The hour card converts pace to sellable kWh live
Where it stops
- No duty cycles or efficiency chain
- Single interval — no varying-power profiles
Practical Use Cases
Motoring
compare motor ratings in honest watts
Home energy
pace into kWh the meter actually sells
Teaching
rate versus amount, made live
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Power Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
What is the difference between work and power?
Work is the amount of energy transferred; power is how fast. Carry the same groceries up the same stairs slowly or quickly and the WORK is identical — the fast trip costs more POWER because the same joules arrived in less time. Engines advertise power because pace is what you feel; the stairs only ever billed the amount.
Why does the page derive horsepower instead of using 746?
Because 746 is a rounded convention for electrical rating plates, while the mechanical horsepower is EXACTLY 550 foot-pounds per second — and with the international pound and foot plus standard gravity all exact, that is 745.699871582270 watts, no rounding anywhere. Two definitions circulate; this page names the one it uses and shows its arithmetic.
What is a kWh, in this page's language?
A pace times an hour: 1,000 W sustained for 3,600 s moves 3,600,000 J. The meter sells energy, not power — kWh is just joules in bulk packaging (one kWh = 3.6 million J). The hour card on this page is that conversion computed from YOUR pace.
Can power be negative?
Yes — it means energy is being removed at that rate: the engine braking downhill, the dynamo charging. The sign is the direction of transfer, exactly as with work; the page prints it rather than tidying it away.
Why is dividing by zero refused?
Because 5,000 J in NO time is not a big power, it is no pace at all — an unbounded rate that no device, wire or drivetrain can carry. Refusing the instant is the honest answer; a page that printed a number there would be selling the infinite quietly.
How do watts compare across machines fairly?
At the same energy: the pump that moves the same water in half the time is twice the power, full stop. Comparing paces while quietly changing the amounts is the oldest advert trick on the page — anchor on the joules first, then let the seconds talk.
Where does P = F·v fit?
It is this page's law with the work rewritten: W = F·d, so P = F·d/t = F·v. It says a car's power need grows with speed for the same drag force — and it is why doubling speed costs far more than twice the engine, once the kinetic-energy square has had its say too.
Is horsepower why cars feel fast?
Half of it. Acceleration is force over mass (the force page's bill); power caps how long that force can be sustained as speed builds, since P = F·v. Peak horsepower is the size of the tap; the car's mass decides how the water feels.