# Ratio of 3 Numbers Calculator

Simplify a three-part ratio, convert to percentages, and scale to any total. Free online 3-number ratio calculator for mixing, recipes, and math.

## What this calculates

Simplify any three-part ratio to its lowest terms, see the percentage breakdown, and scale the parts to a specific total. Perfect for mixing recipes, splitting costs, or solving math problems involving three quantities.

## Inputs

- **Part A** — The first part of the three-part ratio.
- **Part B** — The second part of the three-part ratio.
- **Part C** — The third part of the three-part ratio.
- **Scale Total To** — Scale the three parts so they add up to this total.

## Outputs

- **Simplified Ratio** — formatted as text — The three-part ratio in its simplest whole-number form.
- **Percentages** — formatted as text — Each part as a percentage of the total.
- **Decimal Ratio** — formatted as text — Each part expressed as a decimal relative to the first part.
- **Scaled Values** — formatted as text — Parts scaled to the specified total.
- **Original Total** — The sum of the three original values.

## Details

A three-part ratio like 2:3:5 describes how three quantities relate to each other. Simplifying a three-part ratio works the same way as a two-part ratio: divide all three parts by their greatest common divisor (GCD).

**How to Simplify a Three-Part Ratio:**

For the ratio 12:18:24, find the GCD of all three numbers. GCD(12, 18, 24) = 6. Divide each part by 6 to get 2:3:4.

**Converting to Percentages:**

Add all three parts together and divide each part by the total. For 2:3:5, the total is 10. The percentages are 20%, 30%, and 50%.

**Scaling to a Total:**

If a concrete mix ratio is 1:2:3 (cement:sand:gravel) and you need 600 kg total, each unit equals 600/6 = 100 kg. That gives you 100 kg cement, 200 kg sand, and 300 kg gravel.

**Common Uses:**

Three-part ratios appear in concrete mixing (1:2:4), color mixing (RGB values), investment allocation, and recipe scaling. Understanding how to work with them saves time and prevents errors.

## Frequently Asked Questions

**Q: How do I simplify a ratio with 3 numbers?**

A: Find the greatest common divisor (GCD) of all three numbers and divide each part by it. For example, 15:25:35 has a GCD of 5, so it simplifies to 3:5:7. If the numbers contain decimals, multiply all parts by a power of 10 first to make them whole numbers, then simplify.

**Q: How do I convert a 3-part ratio to percentages?**

A: Add all three parts to get the total, then divide each part by the total and multiply by 100. For the ratio 2:3:5, the total is 10. The percentages are (2/10) x 100 = 20%, (3/10) x 100 = 30%, and (5/10) x 100 = 50%.

**Q: Can I scale a three-part ratio to a specific total?**

A: Yes. Divide your desired total by the sum of the simplified ratio parts, then multiply each part by that factor. For a ratio of 1:2:3 scaled to 180, each unit = 180/6 = 30, giving you 30:60:90.

**Q: What is the difference between a ratio and a proportion with three numbers?**

A: A ratio like 2:3:5 shows the relative size of three quantities. A proportion is an equation stating that two ratios are equal. With three-part ratios, you can still set up proportions to solve for unknowns, such as finding the third value when you know the ratio and two of the three actual amounts.

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Source: https://vastcalc.com/calculators/math/ratio-of-3-numbers
Category: Math
Last updated: 2026-04-08