Ratio Calculator

Use this professional-grade ratio calculator to simplify ratios, solve proportions, scale a ratio to a target value, or split a total by a ratio. Designed for students, educators, analysts, and creatives, it provides instant, precise results with full accessibility and mobile-first ergonomics.

Interactive Calculator

Choose calculator mode

Simplify a ratio

You can enter integers or decimals. We remove decimals automatically before simplifying.
Zero is allowed, but not both terms zero. Example: 5:0 simplifies to 1:0.

Results

Enter values to see results. The results panel is reserved for output to prevent layout shift.

Authoritative Content Ecosystem

Data Source and Methodology

Authoritative Data Source: ISO 80000-2:2019 — Quantities and units — Part 2: Mathematics. International Organization for Standardization (2019). Direct link: https://www.iso.org/standard/64973.html.

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

Simplifying a ratio a:b using the greatest common divisor (GCD):

$$\text{Let } g=\gcd(a,b)\ ,\quad a:b \equiv \frac{a}{g}:\frac{b}{g}$$

Equivalence of ratios and cross-multiplication:

$$\frac{a}{b}=\frac{c}{d}\ \Longleftrightarrow\ ad=bc$$

Solving for the missing term:

$$a=\frac{bc}{d},\quad b=\frac{ad}{c},\quad c=\frac{ad}{b},\quad d=\frac{bc}{a}$$

Scaling a ratio to match a target value T on term a (factor k=T/a):

$$k=\frac{T}{a},\quad (a',b')=(ka,kb)$$

Splitting a total T by a:b:

$$x=\frac{a}{a+b}\,T,\quad y=\frac{b}{a+b}\,T$$

Glossary of Variables

  • a, b: The two terms forming a ratio a:b.
  • c, d: The terms of a second ratio c:d for a proportion a:b = c:d.
  • GCD: Greatest common divisor, the largest integer that divides two integers.
  • k: Scaling factor applied to both terms of a ratio.
  • T: Total amount to split according to a ratio.
  • x, y: Parts of T corresponding to terms a and b respectively.

How It Works: A Step-by-Step Example

Example: Simplify 18:24, scale so the first term equals 21, and split T=350 by the simplified ratio.

  1. Compute GCD(18,24)=6, so 18:24 → 3:4.
  2. Scale 3:4 to set a=21. Factor k=21/3=7 → 21:28.
  3. Split T=350 by 3:4. Sum is 7. Parts are x=350·3/7=150 and y=350·4/7=200.

Frequently Asked Questions (FAQ)

What is a ratio?

A ratio compares two quantities a and b, often written as a:b or a/b. Two ratios are equivalent if one is a constant multiple of the other.

How do I compare two ratios?

Convert both to the same form (e.g., reduced form or decimal a/b). If their reduced forms match, they are equivalent. The tool can simplify each ratio for a direct comparison.

Can I enter negative numbers?

While ratios typically compare non-negative quantities, the math works with signed values. The tool handles signs consistently and shows the simplest exact result.

What happens if a term is zero?

If one term is zero, the simplified form is 0:1 or 1:0 (for nonzero counterpart). The proportion solver prevents division by zero and will guide you to correct inputs.

Will rounding affect proportions?

Yes, rounding can slightly change the exact proportion. The scaler shows both exact and rounded results so you understand any deviation introduced.

Do you store my inputs?

No. All calculations are performed locally in your browser for privacy and speed.

Tool developed by Ugo Candido. Content verified by CalcDomain Editorial Board.
Last reviewed for accuracy on: .