Ratio Calculator

Simplify ratios, find missing values, and compare ratios to find equivalents.

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Simplified Ratio

2:3

Original12:18
Simplified2:3
As 1:n1:1.5
As fraction12/18 = 2/3

How to Use the Ratio Calculator

  1. Simplify a ratio. Enter two numbers separated by the colon. The calculator finds the Greatest Common Factor (GCF) and divides both sides by it. Example: 12:18 has GCF of 6, so 12/6 = 2 and 18/6 = 3, giving the simplified ratio 2:3. The result also shows the ratio as 1:n and as a fraction.
  2. Scale a ratio. Enter the base ratio and a scale factor to proportionally increase or decrease both values. Useful for scaling recipes (triple a 2:3 ratio to get 6:9) or architectural plans (1:50 scale means 1 cm = 50 cm).
  3. Solve for a missing value. Enter three known values in the proportion a:b = c:? format and leave the unknown blank. The calculator uses cross-multiplication to find the missing fourth value. Example: 3:4 = 9:? gives ? = (4 × 9) / 3 = 12.

Ratio Formulas and Applications

Simplify ratio a:b:    divide both by GCF(a, b)

Scale ratio a:b by f:  (a × f):(b × f)

Solve proportion:      a:b = c:d
Cross-multiply:        a × d = b × c
Find d:                d = (b × c) / a
Find c:                c = (a × d) / b

Real-world ratio applications:

ApplicationRatioMeaning
Concrete mix1:2:31 part cement, 2 sand, 3 gravel
Map scale1:50,0001 cm = 50,000 cm = 500 m
Recipe scale2:3 eggs to cups4 eggs needs 6 cups
Aspect ratio (HD)16:91920px × 1080px
Gear ratio3:13 engine turns per 1 wheel turn
Debt-to-equity1.5:1$150K debt per $100K equity

Frequently Asked Questions

A ratio compares two (or more) quantities showing their relative sizes. The ratio 3:4 means for every 3 of the first quantity, there are 4 of the second. Ratios can be written three ways: 3:4, 3/4, or as the decimal 0.75. They appear in cooking (1:2 oil to vinegar for dressing), construction (1:2:3 concrete mix), maps (1:50,000 scale), and finance (price-to-earnings ratios). Unlike fractions, ratios compare parts to parts, not parts to a whole.

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