Simplify ratios to lowest terms, solve for unknown values, and scale ratios up or down. Perfect for recipes, map scales, aspect ratios, blueprints, and any proportion problem.
Quick reference for ratio math and common use cases
Use our percentage calculator to work through any ratio or proportion problem instantly.
Open Percentage Calculator →A ratio in its simplest form has no common factor between its parts other than 1. To simplify, divide both parts by their Greatest Common Divisor (GCD):
Step 1: Find the GCD of both numbers using Euclid's algorithm.
Step 2: Divide both parts of the ratio by the GCD.
Example: Simplify 24:36
GCD(24, 36): 36 = 1×24 + 12; 24 = 2×12 + 0. GCD = 12.
24÷12 = 2; 36÷12 = 3. Simplified: 2:3
Another example: 15:25. GCD = 5. 15÷5 = 3; 25÷5 = 5. Simplified: 3:5
When you know three parts of a proportion and need the fourth, use cross-multiplication:
If a:b = c:x, then x = (b × c) ÷ a
Example: A recipe calls for flour and sugar in a 3:2 ratio. If you use 9 cups of flour, how much sugar do you need?
3:2 = 9:x → x = (2 × 9) ÷ 3 = 18 ÷ 3 = 6 cups of sugar
Map scale example: A map scale is 1:50,000. If two cities are 7.5 cm apart on the map, what is the real distance?
1:50,000 = 7.5:x → x = 50,000 × 7.5 = 375,000 cm = 3.75 km
To scale a ratio, multiply or divide both parts by the same number. This preserves the relationship while changing the quantities.
Scaling up: Ratio 1:4 scaled by 6 = 6:24 (still simplifies to 1:4)
Scaling down: Ratio 15:20 scaled down by 5 = 3:4
This is especially useful for recipe scaling. If a batter recipe uses 2 cups flour : 3 cups milk : 1 egg and you want to triple it: 6 cups flour : 9 cups milk : 3 eggs. All parts multiply by 3, preserving the taste and texture relationship.
Aspect ratios describe the proportional relationship between width and height of a display or image. Understanding them helps when cropping photos, setting up video exports, or buying monitors:
16:9 — Universal widescreen standard. All HD (1920×1080) and 4K (3840×2160) TVs and monitors use this. YouTube, Netflix, and most streaming services produce 16:9 content.
4:3 — Traditional TV and monitor format, now mainly used for legacy content and some video conferences.
1:1 — Square format, popularized by Instagram. Each pixel dimension is equal.
9:16 — Vertical/portrait video for TikTok, Instagram Reels, and YouTube Shorts.
21:9 — Ultrawide cinema format used in some premium monitors and films.
3:2 — Common in DSLR camera sensors and some smartphones.
Ratios appear constantly in daily situations: Cooking — recipes are defined by ingredient ratios that must be preserved when scaling. A 2:1 water-to-rice ratio remains 2:1 whether you're cooking one cup or ten. Construction — concrete mix ratios (cement:sand:aggregate = 1:2:3) ensure structural integrity. Finance — price-to-earnings (P/E) ratios compare stock price to earnings. Debt-to-equity ratios measure financial leverage. Photography — f-stop and shutter speed relationships form ratios that control exposure. Medicine — drug dosages are often expressed as mg per kg of body weight — a ratio scaled to patient size.
A ratio a:b can be expressed as a fraction (a/b) or as a percentage of the total (a/(a+b) × 100 for the first part).
Example: Ratio 3:7. Fraction: 3/7 ≈ 0.4286. As percent of total: 3/(3+7) = 30% for the first part, 70% for the second.
This is useful in finance when splitting investments: a 60:40 stock/bond split means 60% stocks and 40% bonds.
Divide both numbers by their GCD. Ratio 12:8 → GCD is 4 → 12÷4:8÷4 = 3:2. Use Euclid's algorithm to find GCD: divide larger by smaller, take remainder, repeat until 0.
Cross-multiply. If a:b = c:x, then x = (b×c)÷a. Example 3:4 = 9:x → x = (4×9)÷3 = 12.
16:9 (HD/4K widescreen), 4:3 (traditional TV), 1:1 (square/Instagram), 9:16 (vertical mobile video), 21:9 (ultrawide). 16:9 is the current universal standard.
Multiply or divide both parts by the same number. Ratio 2:3 scaled by 4 = 8:12 (still equivalent). Ratio 10:15 scaled down by 5 = 2:3. The relationship stays identical.