How to Use the Ratio Calculator
The ratio calculator helps you work with ratios in three modes: find a missing value in a proportion, simplify a ratio to its lowest terms, or compute golden ratio dimensions. It supports plain numbers, world currencies (including US dollar and Russian ruble), metric units, and US imperial units.
Mode 1: Find Missing Value (A : B = C : D)
A ratio is a relationship between two quantities, like a fraction. The ratio calculator solves proportions — two equivalent ratios set equal to each other. Enter any three of the four values A, B, C, D and leave one blank; the calculator finds the missing fourth value.
Example: You have the ratio 3 : 8 and want an equivalent ratio with denominator 72.
- Enter A = 3, B = 8, C = blank, D = 72
- The calculator solves: C = A × D ÷ B = 3 × 72 ÷ 8 = 27
- So 3 : 8 = 27 : 72 ✓
Formula (cross-multiplication):
- Find A: A = B × C ÷ D
- Find B: B = A × D ÷ C
- Find C: C = A × D ÷ B
- Find D: D = B × C ÷ A
Mode 2: Simplify a Ratio
Enter two values A and B to reduce the ratio A : B to its simplest (lowest) form. The calculator finds the Greatest Common Divisor (GCD) and divides both values by it.
Example: Simplify 12 : 8
- GCD(12, 8) = 4
- 12 ÷ 4 : 8 ÷ 4 = 3 : 2
Mode 3: Golden Ratio
The golden ratio (φ ≈ 1.6180339887) is a special mathematical constant found throughout nature, art, and architecture. It is defined by the proportion:
(A + B) / A = A / B = φ ≈ 1.618
Enter length A (the larger segment) and the calculator returns:
- B = A ÷ φ (the smaller segment)
- A + B (the total length)
- Verification: (A+B)/A and A/B both equal φ
The golden ratio appears in the Fibonacci sequence, the proportions of the Parthenon, Da Vinci's paintings, and the spiral of nautilus shells. A rectangle with sides in the golden ratio is called the golden rectangle — considered by many to be the most aesthetically pleasing shape.
Units Supported
You can work with ratios in any of these unit systems:
- Plain Numbers — no unit labels
- Currencies — USD ($), RUB (₽), EUR (€), GBP (£), JPY (¥), CNY, CAD, AUD, CHF, INR, BRL, KRW, MXN, TRY, SEK, NOK, PLN
- Length — Metric: meters (m), centimeters (cm), kilometers (km)
- Length — Imperial: feet (ft), inches (in), miles (mi), yards (yd)
- Weight — Metric: kilograms (kg), grams (g), metric tons (t)
- Weight — Imperial: pounds (lb), ounces (oz)
- Volume — Metric: liters (L), milliliters (ml)
- Volume — Imperial: gallons (gal), fluid ounces (fl oz), quarts (qt)
Frequently Asked Questions
What is a ratio?
A ratio is a comparison of two quantities by division, written as A : B or A/B. For example, if a pie has 8 slices and 3 were eaten, the ratio of eaten slices to total is 3 : 8.
What is the golden ratio?
The golden ratio is approximately 1.618033…, often denoted φ (phi). It appears when a line is divided into two segments so that the longer part divided by the shorter part equals the whole length divided by the longer part. It is widely found in nature, art, and design.
How do I find a missing ratio value?
Set up the proportion A : B = C : D. Use cross-multiplication: A × D = B × C. Rearrange to find the missing variable. The calculator does this automatically when you leave one field blank.
What does simplifying a ratio mean?
Simplifying a ratio means expressing it with the smallest possible whole numbers while keeping the same relationship. It is done by dividing both parts by their Greatest Common Divisor (GCD).