The one method behind every conversion
Every conversion multiplies by one in disguise: a fraction whose top and bottom name the same quantity, like 2.54 cm over 1 inch. Multiplying changes the units without changing the amount, and chaining fractions converts anything to anything. Miles to kilometres to metres is just two such multiplications, with each old unit cancelling like a number.
Set it up so unwanted units cancel diagonally and the wanted unit survives. Converting 5 miles: multiply by 1.609344 km per mile and miles cancel, leaving 8.05 km (5 times 1.609344). Mistakes come from flipped fractions, so estimate first: a mile exceeds a kilometre, so the kilometre number must be bigger.
- Multiply by fractions equal to one, like 2.54 cm per inch
- Arrange units to cancel; survivors are the answer's units
- Estimate direction first: bigger unit means smaller number
Length: inches, feet, miles, and metric
The anchors are 1 inch equals 2.54 cm exactly, 1 foot equals 30.48 cm, and 1 mile equals 1.609344 km. A person at 5 feet 9 inches stands 69 inches, and 69 times 2.54 gives 175.26 cm, usually rounded to 175. A marathon's 26.2 miles times 1.609344 lands at 42.16 km, matching the official 42.195 km race.
For mental math, memorize three approximations: an inch is about 2.5 cm, a foot about 30 cm, and a mile about 1.6 km. Five miles is roughly 8 km, ten feet roughly 3 metres, and a 6-foot person roughly 183 cm (72 times 2.54 is 182.88). Approximate for conversation, then compute exactly for construction, medicine, and fittings.
- 5 ft 9 in equals 69 in equals 175.26 cm
- 26.2 miles equals 42.16 km, the marathon distance
- Quick estimates: inch 2.5 cm, foot 30 cm, mile 1.6 km
Weight and volume: pounds, ounces, cups, litres
Weight hinges on 1 pound equals 0.45359237 kg and 1 ounce equals 28.35 g. A 150 lb person weighs 68.04 kg (150 times 0.45359237), and a 500 g flour bag is about 17.6 ounces (500 divided by 28.35). Kitchen scales that toggle grams beat scoops: a cup of flour varies 20 percent by packing, while 120 g is always 120 g.
Volume adds the US cup at 236.59 ml, tablespoon at 14.79 ml, teaspoon at 4.93 ml, and US gallon at 3.785 L. Two cups make about 473 ml, four tablespoons make a quarter cup, and three teaspoons make one tablespoon. The trap: a US cup (236.59 ml) differs from the metric cup (250 ml) in many Commonwealth recipes, so check which cup yours means.
- 150 lb equals 68.04 kg; 1 oz equals 28.35 g
- 1 US cup 236.59 ml; 1 tbsp 14.79 ml; 1 tsp 4.93 ml
- Bake by grams; US cup and metric cup differ
Temperature: the two formulas that matter
Celsius to Fahrenheit is F equals C times 9 over 5 plus 32; the reverse is C equals (F minus 32) times 5 over 9. Room temperature of 20 C becomes 68 F (20 times 1.8 plus 32), and (68 minus 32) times 5 over 9 returns exactly 20 C. Body temperature of 98.6 F converts to 37.0 C (66.6 times 5 over 9), the anchor every thermometer checks.
Ovens reward memorization: 350 F is about 177 C ((350 minus 32) times 5 over 9 equals 176.67), 400 F about 204 C, and 180 C is 356 F, close enough to 350 F for most recipes. Remember interval sizes differ: one Celsius degree spans 1.8 Fahrenheit degrees, so a 10 C weather swing is a dramatic 18 F change.
- F = C x 9/5 + 32; C = (F - 32) x 5/9
- 20 C = 68 F; body 98.6 F = 37.0 C
- Oven anchors: 350 F near 177 C; 180 C near 356 F
Speed: km/h, mph, and metres per second
Road speed pivots on 1 mile equals 1.609344 km. A cruise of 100 km/h equals 62.14 mph (100 times 0.621371), while a 60 mph highway limit equals 96.56 km/h (60 times 1.609344). Science prefers metres per second: divide km/h by 3.6, so 100 km/h is 27.78 m/s.
Runners live in pace, the inverse of speed: a 5-minute kilometre is 12 km/h (60 divided by 5), and a 30-minute 5K averages exactly 10 km/h. Drivers crossing borders should memorize three pairs: 50 km/h is about 31 mph, 100 km/h about 62 mph, and 120 km/h about 75 mph.
- 100 km/h equals 62.14 mph equals 27.78 m/s
- 60 mph equals 96.56 km/h; 50 km/h is about 31 mph
- To m/s divide km/h by 3.6; switch dash units at borders
Conversion mistakes everyone makes
Mixing US and imperial units tops the list: a US gallon at 3.785 L is 20 percent smaller than an imperial gallon at 4.546 L, so cross-country fuel comparisons silently break. Confusing fluid ounces (volume, 29.57 ml) with weight ounces (mass, 28.35 g) curdles recipes and misleads shoppers.
Subtler errors are power mistakes: a square foot is 929 square cm, not 30.48, because area scales with the square of length, and a cubic metre holds 1,000 litres, not 100. Convert the unit first, then apply the power. And round only at the end: rounding 2.54 to 2.5 mid-chain across five steps compounds into a visibly wrong answer.
- US gallon 3.785 L vs imperial 4.546 L; confirm country
- Fluid ounces are volume; weight ounces are mass
- Round once at the end, never inside a chain
Quick conversion tables and FAQs
Pin these pairs: 5 ft is 152.4 cm, 5 ft 6 in is 167.64 cm, 6 ft is 182.88 cm; 130 lb is 58.97 kg, 150 lb is 68.04 kg, 180 lb is 81.65 kg; 30 C is 86 F, 25 C is 77 F, 0 C is 32 F; 5 km is 3.11 miles, 10 km is 6.21 miles, 100 miles is 160.93 km. Each follows from the anchors: 66 inches times 2.54 is 167.64, and 180 times 0.45359237 is 81.65.
Which habit helps most? Typing the full unit string, like 5 ft 9 in to cm, because bare numbers invite the wrong factor. Grams and millilitres suit baking precision, cups suit weeknight speed. Match precision to the input: a 150 lb body weight deserves 68 kg, not 68.0388555 kg.
- Height: 5 ft 152.4 cm; 5 ft 6 in 167.64 cm; 6 ft 182.88 cm
- Weight: 130 lb 58.97 kg; 150 lb 68.04 kg; 180 lb 81.65 kg
- Match precision to inputs; drop phantom decimals