Math Playground

Measurement › US customary

US customary units

Inches, feet, miles · ounces, pounds, tons · cups, quarts, gallons · acres, Fahrenheit. The system that runs daily life in the US.

US customary units

Pick a family — bars are scaled by how big each unit really is (log-shrunk where needed).

in
inch — thumbtip to first knuckle
1 in
ft
foot — 12 in, length of a US ruler
12 in
yd
yard — 3 ft, walking step
36 in
mi
mile — 5280 ft, ~15 min walk
63,360 in

Why does the US still use these?

Most of the world (95% of it) uses the metric system — clean powers of 10, easy to convert. The US sticks with units that evolved from medieval English measures: a foot is roughly a man's foot, a yard is roughly a stride, a gallon is roughly a stable bucket. The numbers are weird (12, 3, 1760, 16, 128) because they were chosen for easy practical division — feet by halves, thirds, quarters; gallons by quarter-quarts.

Length

  • 12 inches = 1 foot — the printed ruler everyone grew up with.
  • 3 feet = 1 yard — about a confident step.
  • 5280 feet = 1 mile — yes, a strange number. It's from the Roman mille passus (1000 paces).

A useful mental anchor: an American football field, end zones included, is 120 yards = 360 feet ≈ 110 metres.

Weight

  • 16 ounces = 1 pound. Roughly a pint of water.
  • 2000 pounds = 1 short ton. The "ton" the US almost always means.
  • (Confusingly, the UK has a long ton = 2240 lb, and the metric world has a tonne = 1000 kg ≈ 2204.6 lb.)

Mass vs weight (briefly)

Scientifically, mass and weight differ — mass is how much stuff, weight is how hard gravity pulls on it. In everyday US usage they're treated the same; "ounce" and "pound" are mass units that get called weight.

Volume

  • 8 fl oz = 1 cup. A standard measuring cup.
  • 2 cups = 1 pint. (Mnemonic: "a pint's a pound the world around" — close enough for water.)
  • 2 pints = 1 quart. A typical milk carton.
  • 4 quarts = 1 gallon. The big jug.

US gallon ≠ UK gallon

The UK imperial gallon is 1.2 times bigger than the US gallon (4.546 L vs 3.785 L). Imperial fluid ounces and pints differ too. When converting recipes from across the Atlantic, check which gallon a number refers to.

Area

  • 144 sq in = 1 sq ft — because 12 × 12.
  • 9 sq ft = 1 sq yd — because 3 × 3.
  • 43,560 sq ft = 1 acre — historically the area one ox could plough in a day. About 90% of a US football field.
  • 640 acres = 1 sq mile — a US "section" of land, still used in surveys.

Temperature — Fahrenheit

  • Water freezes at 32°F.
  • Pleasant room is 68–72°F.
  • Body temperature is 98.6°F (37°C).
  • Water boils at 212°F.

Convert with °C = (°F − 32) × 5/9 and °F = °C × 9/5 + 32. They cross at exactly −40°.

Try it

  1. How many cups in a gallon?
  2. How many sq ft in an acre? (Round answer.)
  3. A 6-foot fence is how many inches tall?
  4. Is 1.5 lb more or less than 1 kg?

Answers: 1) 16 cups. 2) 43,560 sq ft. 3) 72 in. 4) Less — 1 kg is about 2.2 lb, so 1.5 lb is only about 0.68 kg.