Physics I: Mechanics › Work & energy › full formula sheet
Say it: “one watt equals one joule per second”
The watt
The unit of power — what a watt means, where it came from (James Watt's horses), and how to convert it.
The watt (W) is the SI unit of power — the rate of energy flow. Bigger units: kW (10³), MW (106). Legacy unit: horsepower, 1 hp ≈ 746 W.
Before this lesson: Power
Where it comes from
In the 1780s James Watt needed to sell steam engines to mine owners who thought in horses. So he measured what a horse could sustain — about 746 watts — and priced his engines in “horsepower.” The marketing worked so well that the SI unit of power now bears his name.
You can't — different quantities. 60 W is a rate (60 joules every second); 60 J is an amount. Comparing them is like comparing speed to distance. The watt's whole job is to keep the rate separate from the amount:
Derivation
The watt isn't derived from physics — it's defined from the power formula. But the definition chain is worth seeing once:
Scale ladder: phone charger ~20 W → human ~100 W → microwave ~1000 W (1 kW) → car ~100 kW → locomotive ~3 MW → power station ~1 GW. Pin a few rungs and absurd answers stand out.
How to use it
The procedure, every time:
- Identify rate vs amount. W, kW, MW, hp → power (rate). J, kWh → energy (amount). Never mix them.
- Convert prefixes. kW → W: ×1000. MW → W: ×1,000,000. W → kW: ÷1000.
- Horsepower: ×746. hp → W: multiply by 746. W → hp: divide by 746.
- Energy from power: E = P × t. Watch t's units: seconds for joules, hours for Wh/kWh.
- Sanity-check against the ladder. A “phone charger” at 20 kW is wrong by 1000× — the scale ladder catches it.
Worked examples
Four problems, easiest first. Rate vs amount, every time.
Example 1 — energy from power: 60 W bulb for 10 s
- Rate × time. E = P × t = 60 × 10 = 600 J.
- Read it. 60 joules every second, for 10 seconds: 600 joules total.
Your turn — 100 W device for 30 s. Energy?
Answer: 3000 J. 100 × 30 = 3000 J.
Example 2 — prefix: 2.5 kW motor in watts
- Convert. 2.5 kW = 2.5 × 1000 = 2500 W.
- Interpret. 2500 joules per second — a serious motor.
Your turn — 0.8 kW in watts?
Answer: 800 W. 0.8 × 1000 = 800 W.
Example 3 — horsepower: 2 hp engine in watts
- Convert. 2 × 746 = 1492 W (≈ 1.5 kW).
- Context. Two actual horses' sustained output — modest by car standards (a sedan is ~100+ kW).
Your turn — 1.5 hp in watts?
Answer: 1119 W. 1.5 × 746 = 1119 W.
Example 4 — slow drain: 20 W phone charger for 2 hours
- Time in seconds. 2 h = 7200 s.
- Energy. E = 20 × 7200 = 144,000 J (144 kJ, or 0.04 kWh).
- Check. Small power × long time = modest energy. ✓
Your turn — 10 W router for 1 hour. Energy in joules?
Answer: 36,000 J. 10 × 3600 = 36,000 J.
Memorization tips
- Say it aloud: “a watt is a joule per second — rate, not amount.”
- The ladder: 20 W charger, 100 W human, 1 kW microwave, 100 kW car, MW locomotive, GW power station. Absurd answers stick out.
- k = 1000, M = 1,000,000. Count zeros deliberately — prefix slips are the #1 watt error.
- hp ≈ 746 W. ≈ ¾ kW — close enough for estimates.
- Rate × time = amount: W×s = J; kW×h = kWh. Match the time unit to the energy unit you want.
- 'Per hour' is banned: watts are already per-second. Never say watts per hour.
Final challenge
Five mixed questions — conversions, rate vs amount, and the ladder. Score 5/5 and the watt is yours.
← Back to the Physics I formula sheet
How to learn a formula here
- Read each section in order — every section ends with a short quiz. Take it before moving on; the questions test exactly what you just read.
- Work the examples with the answers covered, then uncover one step at a time and compare.
- Finish with the final challenge — five mixed questions including the classic traps.
- Retake what you miss — every quiz reshuffles each attempt, and every answer explains itself.
Frequently asked questions
Is a watt a unit of energy?
No — it's the unit of power (rate). Energy is the joule. A 100 W device uses 100 J every second; run it an hour and the energy is 360,000 J. Rate vs amount.
Why is it called a watt?
After James Watt (1736–1819), whose steam engines industrialized Britain. He marketed them in 'horsepower' — about 746 W per horse — and the SI unit took his name in 1960.
How many watts is a horsepower, exactly?
1 mechanical horsepower = 745.7 W, universally rounded to 746 W. (Metric horsepower is 735.5 W — a slightly different legacy unit. Physics classes use 746.)
What's bigger: a kW or a kWh?
Trick question — different quantities. A kW is power (1000 J/s); a kWh is energy (3.6 MJ). It's like asking whether 60 mph is bigger than 60 miles.
How many watts does a human produce?
About 100 W sustained (a bright bulb), up to ~1000 W in a brief sprint. Useful scale anchors: if your answer says a person outputs 10 kW all day, something broke.
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