CalculatorShelf
Browse calculators
Browse by shelf

Choose a focused collection, or open the complete directory.

All calculators
StoragePlan capacity, performance, and reliability decisions for storage and PC hardware.Home ProjectsEstimate materials and quantities for practical home projects with visible assumptions.Pool & WaterEstimate pool volume from measured dimensions; use the guides to understand product and safety boundaries.ShippingEstimate shipping quantities, costs, and loading geometry before requesting a quote.LifestyleHandle everyday sizing, photography, wrapping, and seasonal planning questions.SportsExplore pace, motion, and sizing calculations with explicit assumptions and limits.BusinessPlan margin and language-service decisions from entered prices, costs, and volumes.Math & EducationCalculate arithmetic, scientific expressions, units, dates, algebra, physics, and education formulas with visible methods.FinanceCompare currency, bills, discounts, and fixed-rate loan scenarios with visible rates, rounding, and assumptions.
All calculatorsMethodology

Ratio Calculator

Simplify a ratio, solve A:B = C:x, build an equivalent ratio table, or find y from direct (y = kx) or inverse (y = k/x) variation, with the constant k.

Interactive calculator · Method RATIO-SOLVER-1.0 · Last reviewed: 2026-11-04

Calculate your scenario

Simplify: scale A and B to whole numbers (up to 6 decimal places) and divide both by their greatest common factor.

Your inputs

Try an example

Default worked example. Edit the inputs to calculate your scenario.

Default worked example

Answer 2:3
Simplified A:B 2:3
Constant k 1.5 (k = B ÷ A)
A ÷ B 0.666667

12:18 divided by its greatest common factor is 2:3.

How to use the calculator

Choose a mode, then enter A and B (or x₁ and y₁) and, for a proportion or variation, C (or x₂).

What the result means

12:18 simplifies to 2:3, so B is 1.5 times A; the same ratio solved as 12:18 = 30:x gives x = 45.

Formula and units

Simplify: scale A and B to whole numbers (up to 6 decimal places) and divide both by their greatest common factor. Proportion A:B = C:x gives x = B × C ÷ A. Equivalent ratios are n × (simplified A):n × (simplified B). Direct variation: k = y₁ ÷ x₁ and y₂ = k × x₂. Inverse variation: k = x₁ × y₁ and y₂ = k ÷ x₂.

Worked examples

Simplify 12:18: A (or x₁): 12 dimensionless; B (or y₁): 18 dimensionless; C (proportion) or x₂ (variation): 30 dimensionless; Calculate: simplify.
Example result: Answer: 2:3; Simplified A:B: 2:3; Constant k: 1.5 (k = B ÷ A); A ÷ B: 0.666667.

Inverse variation: 4 workers take 12 days, how long for 6: A (or x₁): 4 dimensionless; B (or y₁): 12 dimensionless; C (proportion) or x₂ (variation): 6 dimensionless; Calculate: inverse.
Example result: Answer: y₂ = 8; Simplified A:B: 1:3; Constant k: 48 (k = x₁ × y₁); A ÷ B: 0.333333.

Limitations and common mistakes

Inputs are non-negative numbers; ratios of measured quantities should use the same units on both sides of a proportion. Direct and inverse variation assume the relationship really is proportional; the calculator does not test that from data. Values shown round to 6 decimal places.

Using direct variation when the quantities vary inversely: more workers finish sooner, so 4 workers taking 12 days means 6 workers take 8 days, not 18.

Sources and assumptions

Method RATIO-SOLVER-1.0; last formula review 2026-11-04. Sources and their supported claims. Calculation methodology.