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Energy you can feel

A kettle in kWh, a phone battery in Wh, a snack in kJ and in kettle boils, the cost of lifting a weight: energy, worked out from a few exact definitions.

  • Number sense
  • Untimed
  • Endless levels

How it plays

Energy is power × time, and a few conversions carry everything: 1 kWh is exactly 3.6 million joules, a food kilocalorie exactly 4,184 J, heating water takes about 4,186 J per kilogram per degree, and lifting takes m × g × h.

Levels go from appliances and phone batteries to food energy as joules and as an average power, to heating water and how long a kettle takes, to lifting, to comparing one with another: how many kettle boils is a biscuit?

Answers are to three significant figures; a typed answer within 10% counts at first, tightening to 3%. The working names each constant and whether it is exact by definition or approximate. The wrong options are the real slips: minutes for hours, watts for kilowatts, the end temperature for the rise.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This builds a feel for everyday quantities of energy and quicker, surer conversions between them. It claims nothing wider.

Learn

How to get better at energy you can feel: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Read which unit the answer wants — kWh, Wh, kJ, W, kcal, minutes or boils — before you look at a single number.
  2. Convert everything into the units that formula wants: watts to kilowatts, minutes to hours, mAh to Ah, a temperature pair to a rise.
  3. Write the one line: power × time, charge × voltage, kcal × 4.184, mass × 4,186 × rise, or mass × 9.81 × height. Then do the arithmetic.
  4. Check the size against something you know: a 2,000 W kettle running for 3 minutes uses 0.1 kWh. So 10 kWh for a 2,000 W heater running 5 minutes means a unit slipped.

Techniques and tricks

  • Friendly minutes as hours

    Learn the minutes that turn into clean fractions of an hour: 3 is 0.05, 6 is 0.1, 12 is 0.2, 15 is 0.25, 20 is ⅓, 30 is 0.5, 45 is 0.75. Then kWh is just kilowatts × that.

    e.g. 800 W for 12 minutes: 0.8 kW × 0.2 h = 0.16 kWh

  • Amp-hours times volts

    A battery’s energy is its charge times its voltage. Divide mAh by 1,000 to get Ah, then multiply by the volts to get Wh.

    e.g. 3,800 mAh at 3.85 V: 3.8 Ah × 3.85 V ≈ 14.6 Wh

  • Times 4, then add the 0.184

    To turn kcal into kJ, multiply by 4 and then add 0.184 of the kcal on top — a little under a fifth of the kcal.

    e.g. 250 kcal: 250 × 4 = 1,000, and 250 × 0.184 = 46, so 1,046 kJ

  • kcal a day to watts

    A day is 86,400 seconds, so a daily amount of kcal in watts is the kcal divided by about 20.65. Divide by 20, then take off about 3%.

    e.g. 2,000 kcal a day: 2,000 ÷ 20 = 100, less 3% ≈ 97 W (exactly 96.9 W)

  • Water: 4.186 kJ per litre per degree

    A litre of water is about a kilogram, so multiply 4.186 by the litres and by the rise. Divide the joules by the kettle’s watts to get seconds.

    e.g. 1 L from 20 °C to 100 °C: 4.186 × 80 = 335 kJ. At 2,000 W: 334,880 ÷ 2,000 ≈ 167 s, about 2.79 min.

  • Lift with 10, then shave 2%

    Work m × 10 × h, which is easy, then take off about 2% for 9.81 instead of 10.

    e.g. 70 kg up 3 m: 70 × 10 × 3 = 2,100 J, less 2% ≈ 2,060 J = 2.06 kJ, which is 2.06 ÷ 4.184 ≈ 0.49 kcal

  • Both sides in joules

    To compare a snack with a kettle, put both in joules and divide. A kettle’s joules are its watts × the seconds it runs.

    e.g. 200 kcal is 200 × 4,184 = 836,800 J. A 2,000 W kettle for 3 minutes is 2,000 × 180 = 360,000 J. About 2.32 boils.

As the levels climb

  • It opens with appliances in kWh and phone batteries in Wh. Next comes food energy, in kJ and as an average power in watts; then heating water and kettle times; then lifting; and last, comparing one with another in kettle boils.
  • Between the new kinds, the numbers grow: appliances run for more hours and then for weeks at a time, batteries grow, snacks get larger, the water climbs to 100 litres and the heights to 300 m. The method is the same; write every unit down so a big number cannot hide a slip.
  • Typed answers must be within 10% at first, then 5%, then 3% from the fourth step of size. At 3%, shortcuts like “divide by 20” need their correction — the 3% they leave out is the whole margin.
  • The time grows a little with the numbers, about 8% a step, so the extra time is for the larger numbers, not for slower thinking.

Traps to avoid

  • Minutes multiplied as if they were hours: 2 kW × 5 = 10 kWh instead of 2 kW × 5/60 ≈ 0.167 kWh. It is 60 times too big, and it is often among the options.
  • Watts left as watts: 2,000 W × 0.083 h answered as 167 kWh. Divide by 1,000 before you multiply by hours.
  • The end temperature used instead of the rise. Heating from 20 °C to 80 °C is a 60-degree rise, not 80.
  • Dividing by 4.184 where you should multiply, or the other way round. kJ are the smaller unit, so the kJ figure is always the bigger number — about four times the kcal.
  • A day taken as 3,600 seconds, or 24 units. Food per day becomes watts only when you divide its joules by 86,400.

How to practise

  • Use “Kinds of question” to drill one formula while it is new — “Heating water” on its own, for example — and add the rest back once it is automatic.
  • Switch “Answer by” to “Typing the answer” when choosing feels easy. The question says how close you must be, and typing stops you picking the one option with sensible units.
  • Raise “Options shown” to see more of the slips at once; for every wrong option, say which unit it forgot to convert.
  • Learn a handful of anchors by heart: 1 kWh = 3.6 million J, 1 kcal = 4,184 J, a day = 86,400 s, water = 4,186 J per kg per °C. Every question here is built from them.

Levels

It is untimed unless you turn the clock on. There is no last level: at least one dial turns without end. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

More number sense

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