Ratio Calculator — Simplify & Solve

A ratio compares two or more quantities. This calculator simplifies ratios to their lowest terms, scales them up or down, and solves for an unknown value in a proportion. Enter values separated by colons, such as 12:8, to simplify, or enter three of the four values in a proportion to find the missing one. Ratios turn up in cooking when a recipe is scaled, in construction when concrete is mixed at 1:2:3, in finance in the form of price-to-earnings ratios, and in map reading, where the printed scale is itself a ratio.

Simplifying means dividing every term by the greatest common divisor. In 12:18 the GCD is 6, which gives 2:3, and in 60:36:24 the GCD is 12, which gives 5:3:2. The calculator shows the divisor it used and finds it with the Euclidean algorithm, where GCD(a,b) equals GCD(b, a mod b). Working the second case through, 60 mod 36 is 24, then 36 mod 24 is 12, then 24 mod 12 is 0, so the divisor is 12. Decimals have to be cleared first, so 0.5:1.5 doubles to 1:3, and mixed units converted, so 50cm:1m becomes 50:100 and then 1:2.

Solving a proportion works the other way round. Given three of the four values, cross-multiplication finds the fourth, and the tool sets that step out so you can check the arithmetic yourself. Scaling a recipe is the everyday case. Simplify 45:60 by its GCD of 15 to get 3:4, then, if the recipe calls for 200 g of flour at 3:4 with sugar, the sugar comes to 200 × (4/3), or 266.67 g. The same working scales a batch up for a party or down for one person.

Money is full of ratios that people rarely name as such. Loan-to-value is the mortgage divided by the property value, so a £160k loan against a £200k house is 80% LTV. Debt-to-income divides monthly debt payments by gross monthly income, and mortgage lenders usually stop at about 40-45%. The price-to-earnings ratio is share price over earnings per share, with the FTSE 100 averaging around 14. The current ratio compares current assets with current liabilities, and anything from 1.5-3 is generally read as healthy. Gearing is debt over equity. Annuity rates are quoted per £1,000 of pot, so £62 a year at age 65 is a 6.2% rate.

Screens and cameras use ratios to describe shape rather than size. 16:9 covers televisions, monitors and YouTube, 4:3 is the legacy shape, 21:9 belongs to cinema and ultrawide monitors, 1:1 to the Instagram square, and 9:16 to vertical phone video and TikTok. A 16:9 1080p panel is 1920×1080 pixels, while 4K UHD at 3840×2160 packs 4× the area. Films are framed at 1.85:1 for standard widescreen and 2.39:1 for anamorphic scope. Still photography settles on 3:2 for a DSLR, 4:3 for compacts and phones, and 1:1 for medium format.

Map scales follow the same notation. An OS Explorer sheet at 1:25,000 puts 1cm to 250m on the ground, an OS Landranger at 1:50,000 puts 1cm to 500m, and the central London A-Z is drawn at 1:8,400, close to 4 inches to 1 mile. Dilution borrows the notation but shifts the meaning, since squash at 1:4 is one part concentrate to four parts water, whereas a 1:10 chemical dilution means one part in ten parts of the finished mixture. Photographers meet ratios as f-stops, where f/2.8 says the aperture diameter is the focal length divided by 2.8, and engineers meet them as gear ratios, where 3:1 means the input wheel turns three times for one turn of the output.

Building materials are specified as ratios too. General-purpose concrete mixes cement, sand and aggregate at 1:3:6, a medium-strength mix at 1:2:4 and a high-strength mix at 1:1.5:3, while a mist coat on new plaster is paint and water at 1:1. Tax bands form ratios of a sort, with the higher rate of 40% sitting at 2× the basic rate of 20%, and pension contributions show the same effect from the other side, because £100 in a pension costs £80 of net pay at the basic rate, £60 at the higher rate and £55 at the additional rate. Stamp duty is banded at 0%, 2%, 5%, 10% and 12%, so the share of the price taken climbs steeply as values rise.