A ratio calculator handles one core task — comparing two or more quantities relative to each other — but that single concept shows up across wildly different contexts: simplifying a basic classroom ratio, finding an image's aspect ratio, working out a gear ratio in mechanical design, or calculating a compression ratio in an engine. This page covers how to calculate ratio in its most general form, then walks through several specific applications: proportions, aspect ratios, gear ratios, compression ratios, and power-to-mass ratios. Browse all calculators if you need a different tool.
How to Calculate Ratio: The Basics
What a Ratio Actually Represents
A ratio expresses how two (or more) quantities relate to each other in relative size — written as A:B, it means "for every A units of the first quantity, there are B units of the second." Unlike a fraction, a ratio doesn't require the two quantities to be parts of the same whole; it's simply a comparison. The same idea of relative size shows up in percentage problems, where one quantity is expressed as a share of another.
Simplifying a Ratio to Lowest Terms
To simplify a ratio, divide both sides by their greatest common divisor (GCD). For example, a ratio of 12:18 has a GCD of 6, so it simplifies to 2:3. This is the same logic used to simplify a fraction, applied to a ratio's two (or more) terms.
Proportion Calculator: Solving for a Missing Value
The Cross-Multiplication Method
A proportion is a statement that two ratios are equal — A:B = C:D. When one value in that statement is unknown, cross-multiplication solves for it:
If A:B = C:D, then A × D = B × C
Example: Solving 3:4 = x:20
3:4 = x:20
3 × 20 = 4 × x
60 = 4x
x = 15
So 3:4 is proportional to 15:20 — this is the exact calculation behind a proportion calculator, used constantly in scaling recipes, converting measurements, and solving similar-figure geometry problems.
Aspect Ratio Calculator: Images, Screens, and Video
Common Aspect Ratios: 3:2, 4:5, and Others
Aspect ratio is simply a ratio applied to width and height — expressed the same way (width:height), and simplified the same way as any other ratio. Some common aspect ratios and their typical uses:
| Aspect Ratio | Common Use |
|---|---|
| 1:1 | Square format (social media posts) |
| 4:5 | Portrait social media posts |
| 3:2 | Standard photography (35mm film heritage) |
| 16:9 | Widescreen video, most modern displays |
| 4:3 | Older TV and monitor format |
How to Know What Your Aspect Ratio Is
To find an image's aspect ratio, divide its width and height by their greatest common divisor, the same simplification process used for any ratio. For example, an image that's 1920 pixels wide by 1080 pixels tall has a GCD of 120, simplifying to 16:9 — the standard widescreen ratio. This image aspect ratio calculator approach works for any pixel dimensions, screen resolution, or print size.
Gear Ratio Calculator
The Gear Ratio Formula
Gear ratio compares the number of teeth on two meshing gears:
Gear Ratio = Number of Teeth on Driven Gear ÷ Number of Teeth on Drive Gear
A drive gear with 12 teeth turning a driven gear with 36 teeth gives a gear ratio of 36 ÷ 12 = 3:1 — meaning the drive gear must rotate three times for the driven gear to complete one full rotation, trading rotational speed for increased torque.
Compression Ratio Calculator
The Compression Ratio Formula
In an internal combustion engine, compression ratio compares the cylinder's total volume (with the piston at the bottom of its stroke) to its volume with the piston at the top:
Compression Ratio = (Swept Volume + Clearance Volume) ÷ Clearance Volume
A higher compression ratio generally allows for more efficient fuel combustion, up to the limits set by the fuel's octane rating and the engine's specific design tolerances.
Power-to-Mass (Power-to-Weight) Ratio Calculator
The Power-to-Mass Formula
Power-to-mass ratio (also called power-to-weight ratio) compares an engine or vehicle's power output to its total mass:
Power-to-Mass Ratio = Power ÷ Mass
This figure is commonly used to compare performance across vehicles of different sizes — a higher power-to-mass ratio generally indicates faster acceleration potential, since less mass needs to be moved per unit of power available.
Waist-to-Height Ratio: A Different Kind of Ratio
Waist-to-height ratio (WHtR) is a health-related ratio that compares waist circumference to height:
Waist-to-Height Ratio = Waist Circumference ÷ Height
This is a genuinely different calculation from the mechanical and image-based ratios covered above — it's a health screening measure, and some research suggests it may reflect abdominal-fat-related health risk more directly than BMI alone for certain populations. This calculator does not compute waist-to-height ratio. As with BMI, this ratio is a screening reference point, not a diagnosis, and is best interpreted alongside a healthcare provider's broader assessment rather than as a standalone health judgment. For a height-and-weight screening number, use the BMI calculator.
Worked Examples: Common Ratios Simplified
A few additional ratio simplification examples:
- 21 as a ratio (e.g., a ratio "of 21") — depends on context, but if comparing 21 to another value like 21:14, simplifying by the GCD of 7 gives 3:2
- 1:2:1 — a three-term ratio (common in mixture or dilution problems) that's already in simplest form, since the GCD of 1, 2, and 1 is 1
- 4:5 ratio — already in simplest form (GCD of 1), commonly seen as a photo/print aspect ratio
- 3:4 ratio — already in simplest form, another common aspect ratio and proportion base
Frequently Asked Questions
How do I calculate a ratio?
Compare two quantities directly as A to B, then simplify by dividing both sides by their greatest common divisor. For example, 12 to 18 simplifies to 2 to 3.
How does a proportion calculator solve for a missing value?
Using cross-multiplication: if A to B equals C to D, then A times D equals B times C. Solving 3 to 4 equals x to 20 gives x equals 15.
How do I find an image's aspect ratio?
Divide the width and height by their greatest common divisor. A 1920 by 1080 pixel image simplifies to a 16 to 9 aspect ratio.
What's the formula for gear ratio?
Gear Ratio equals the number of teeth on the driven gear divided by the number of teeth on the drive gear.
What's the formula for compression ratio?
Compression Ratio equals swept volume plus clearance volume, divided by clearance volume.
How is power-to-mass ratio calculated?
Power-to-Mass Ratio equals power output divided by total mass.
Is waist-to-height ratio the same as a regular ratio calculation?
Mathematically, yes, it is waist circumference divided by height. It is included as a distinct health-related use case, separate from the mechanical and image ratios also covered.
Is this ratio calculator free to use?
Yes. It is free, requires no sign-up, and simplifies or solves ratios instantly.