Ratio Calculator
Work with ratios two ways: reduce a:b to its simplest form with the GCD, or solve a proportion — given a:b = c:x, the calculator cross-multiplies to find the missing x and reports the scale factor and equivalent ratios.
TheCalculators — Ratio Calculator
Printed thecalculators.com
Simplified ratio
4 : 7
divide both terms by GCF(16, 28) = 4
- Given ratio
- 16 : 28
- GCF of terms
- 4
- Simplified
- 4 : 7
- Decimal ratio (a ÷ b)
- 0.571429
- Parts total
- 11 parts
- Share of a
- 36.3636%
Simplifying a : b
- 1Find the GCFGCF(16, 28) = 4 (Euclid’s algorithm)
- 2Divide both terms16 ÷ 4 = 4 · 28 ÷ 4 = 7
- 3Lowest terms4 : 7 — no common factor remains ✓
Equivalent ratios (scaling up)
⚡ Proportion solved: a : b = c : x
- Proportion
- 16 : 28 = 20 : x
- Scale factor (c ÷ a)
- 1.25
- x = b × c ÷ a
- 35
- Solved ratio
- 20 : 35
Solving the proportion, step by step
- 1Cross multiplya · x = b · c → 16·x = 28 × 20 = 560
- 2Isolate xx = 560 ÷ 16 = 35
- 3Check16 / 28 = 0.571429 and 20 / 35 = 0.571429 ✓ equal
Most useful next
Formula
a : b = (a÷g) : (b÷g), g = GCF(a,b) · a:b = c:x → x = b·c ÷ a
Pro tips
- • Ratios are scale-invariant: 16 : 28 and 4 : 7 describe the same relationship — only the units change.
- • To split an amount in ratio a:b, divide it into a+b equal parts; a gets a parts and b gets b parts.
- • Cross-multiplication works because a/b = c/x is just an equality of two fractions.
FAQ
Related Calculators
More Everyday tools you might need.
Fraction Calculator
Add, subtract, multiply or divide two fractions; result simplified with mixed number.
CalculatePercentage Calculator
Three modes: X% of Y, X is what % of Y, and percentage change between two values.
CalculateGreatest Common Factor Calculator
GCF of two numbers via Euclid’s algorithm, plus factor lists, LCM and coprimality.
CalculateLong Division Calculator
Long division with full working: quotient, remainder and 12 decimal places.
Calculate