Aspect Ratio Formula

Derive a ratio from width and height

Let the width be W and the height be H. The decimal aspect ratio is r = W ÷ H. A colon ratio needs the same scale removed from both numbers. For whole-number dimensions, that shared scale is the greatest common divisor, g. The reduced terms are A = W ÷ g and B = H ÷ g, which gives A:B.

The division and the colon notation answer related but different questions. The decimal 1.777777… is convenient for comparison and programming. The exact integer pair 16:9 is better for proportional arithmetic because it keeps both terms visible. Dividing only one dimension is invalid: both sides must be divided by the same nonzero value.

Derive a missing dimension from a known ratio

Suppose the target ratio is A:B, where A is the width term and B is the height term. Every matching frame can be written as kA by kB for one scale factor k. If width W is known, k = W ÷ A. Substituting that value into kB gives H = W × B ÷ A. If height H is known, k = H ÷ B, so W = H × A ÷ B.

Example with a known width: for 16:9 at W = 2560, H = 2560 × 9 ÷ 16 = 1440, giving 2560 × 1440. Example with a known height: for 4:3 at H = 900, W = 900 × 4 ÷ 3 = 1200, giving 1200 × 900. Both results are exact whole-pixel pairs.

Three-step formula verification card

1. 1
   Input

   Enter the ratio terms A:B and a known width W.

2. 2
   Calculate

   Apply H = W × B ÷ A without rounding the intermediate result.

3. 3
   Result

   Cross-check W × B = H × A; equality proves an exact match.

Handle fractional pixels without hiding the error

A formula can be mathematically exact while the result is not a whole pixel. For 16:9 with W = 1366, H = 1366 × 9 ÷ 16 = 768.375. A screen or exported bitmap needs an integer height, so choosing 768 changes the proportion slightly. Verify the rounded pair with cross multiplication: 1366 × 9 = 12,294, while 768 × 16 = 12,288. The difference is 6, so 1366 × 768 is close to 16:9 but not exact.

Keep the unrounded value long enough to make the rounding choice explicit. Floor, nearest, and ceiling can produce different frames. After rounding, verify the final integer pair rather than repeating the check with the discarded decimal.

Choose the right aspect ratio formula

Use W ÷ H when you need a decimal ratio. Use the greatest common divisor when two whole-number dimensions must become the simplest A:B pair. Use H = W × B ÷ A when width is known, or W = H × A ÷ B when height is known. When resizing from original dimensions W₁ × H₁ to a new width W₂, the same relationship becomes H₂ = W₂ × H₁ ÷ W₁.

To check any claimed A:B result, cross-multiply the final dimensions: W × B must equal H × A. This check avoids division rounding and works whether the numbers are small or large. If the products differ, the frame is not exactly the stated ratio.