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Unit conversion

Inches to feet, miles to kilometres, °C to °F, GiB to GB — convert fast, and learn to catch yourself multiplying where you should divide.

  • Number sense
  • Timed
  • 11 levels

How it plays

A quantity in one unit; give it in another. Inside one system first — centimetres to millimetres, hours to minutes — then the imperial ratios, then across systems, then area, speed, data sizes and temperature.

The wrong options are the real mistakes: dividing instead of multiplying, a factor out by ten, 10 used where the ratio is 12, the 32 forgotten in a temperature.

Every factor comes from the unit's definition — an inch is exactly 2.54 cm, a pound exactly 0.45359237 kg — and the working says which one was used.

Keys

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

What it trains

This makes the conversions you practise quicker and surer. It is a skill of its own, not a general one.

Learn

How to get better at unit conversion: 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. Decide the direction first: going to a smaller unit, the number must get bigger; going to a bigger unit, it must get smaller. Say it before you calculate — “feet to inches, more of them”.
  2. Recall the factor as “1 big = k small”: 1 ft = 12 in, 1 mi = 1.609 km, 1 kg = 2.205 lb.
  3. Multiply by k going down to the small unit; divide by k going up to the big one.
  4. Check the answer against the direction you said in step one. That single check catches the most tempting wrong option.

Techniques and tricks

  • Bigger unit, smaller number

    A unit and the count of it move in opposite directions. Fewer of the big ones, more of the small ones — never the same way.

    e.g. 5 ft = 5 × 12 = 60 in; 60 in = 60 ÷ 12 = 5 ft

  • The ratios that are not ten

    These are where a habit of tens trips you: 12 in to a foot, 3 ft to a yard, 1,760 yd to a mile, 16 oz to a pound, 60 s and 60 min, 24 h, 7 days, and 1,024 for KiB, MiB and GiB.

    e.g. 3 lb = 3 × 16 = 48 oz, not 30

  • The exact cross-system anchors

    An inch is exactly 2.54 cm and a foot exactly 0.3048 m. Carry the rest to three or four figures: 1 mi ≈ 1.609 km, 1 kg ≈ 2.205 lb, 1 US gal ≈ 3.785 L, 1 oz ≈ 28.35 g, 1 US cup ≈ 237 ml.

    e.g. 10 in = 25.4 cm; 10 kg ≈ 22.0 lb

  • Miles and kilometres by 1.6

    Miles to kilometres, × 1.6 and a bit; kilometres to miles, ÷ 1.6, or × 0.62.

    e.g. 5 mi ≈ 8.05 km; 8 km ≈ 4.97 mi

  • km/h and m/s by 3.6

    An hour is 3,600 s and a kilometre 1,000 m, so 1 m/s = 3.6 km/h. Divide km/h by 3.6 for m/s; multiply m/s by 3.6 for km/h.

    e.g. 72 km/h = 20 m/s; 25 m/s = 90 km/h

  • Area squares the factor

    A square unit is the length factor squared: 100 m × 100 m = 1 ha = 10,000 m², and 1 km² = 100 ha. A square foot is 0.3048² ≈ 0.0929 m², so 1 m² ≈ 10.76 ft².

    e.g. 25 ha = 25 × 10,000 = 250,000 m²; 45 km² = 4,500 ha

  • Temperature has an offset

    °F = °C × 1.8 + 32, and °C = (°F − 32) ÷ 1.8 — subtract the 32 before dividing. K = °C + 273.15; for °F to K, go through °C.

    e.g. 25 °C = 25 × 1.8 + 32 = 77 °F; 68 °F = (68 − 32) ÷ 1.8 = 20 °C

As the levels climb

  • There are four kinds of conversion, unlocked in turn: within one system (cm to mm, hours to minutes), the imperial ratios and going up to a bigger unit, across systems, and last area, speed, data sizes and temperature.
  • Between them the numbers grow, from single digits to dozens, and the cross-system amounts become awkward multiples like 6 × 15. Work them as the factor times a round number, then adjust.
  • The clock is 7 seconds plus 2 for each kind unlocked and 1 for each step of size, and it closes to 55%. With 11 levels, the ladder has a real top: all four kinds, the largest numbers, the shortest clock.
  • At the last kind the usual mistake is not the arithmetic but the idea: squaring for area, 3.6 for speed, 1,024 against 1,000 for data, the 32 for temperature. Name which idea applies before you touch a number.

Traps to avoid

  • Dividing where you should multiply. 5 ft as 0.417 in is the factor used upside down; the direction check — inches are smaller, so more of them — rules it out.
  • A factor of ten out, or 10 used where the ratio is 12, 16 or 60: 5 ft as 50 in, 3 lb as 30 oz. Ten is the default the mind reaches for.
  • An answer about 10% off. Options 10% either side are there to catch a half-remembered factor: 1.5 instead of 1.609 for miles to km is already 7% low. Learn the factor to three figures.
  • The 32 forgotten, or counted twice: 25 °C as 45 °F or as 109 °F. For °F to °C, take the 32 off first, then divide.
  • GB and GiB treated as the same. 1 GiB is 1,073,741,824 bytes, about 1.07 GB — the gap grows with each step from KiB to MiB to GiB.

How to practise

  • Switch “Answer by” to “Typing the number” once the options feel easy: exact conversions must be exact, and the others are accepted within 1%, so the factor has to be right to three figures.
  • Keep “Options shown” at 4 while the factors are new; raise it to 6 to make the upside-down, ten-times and 10-for-12 slips appear together.
  • When you miss, read the working: it states the factor as “1 big = k small” and the one multiplication or division. Say it in that form until it is how you think.

Levels

Each question has a clock that comes from the work it asks for. There are 11 levels with the default settings, and the counter stops at the real top. 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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