📐 Aspect Ratio Calculator

Simplify a width:height pair to its lowest terms or solve for a missing dimension from a known ratio. The calculator has two modes: Simplify Ratio reduces a pair such as 1920 by 1080 to 16:9, and Solve Dimension takes a ratio you supply plus one known side and returns the other. Both modes show the ratio in decimal form, and Solve mode adds an exact fraction whenever the answer is not a whole number. Six presets cover the ratios most people need.

How to Use

• Choose Simplify Ratio to reduce a width and height to lowest terms, or Solve Dimension to compute a missing side.
• In Simplify Ratio, enter two whole numbers. The simplified ratio and its decimal form update as you type.
• In Solve Dimension, pick a preset such as 16:9 or type your own terms, choose whether to solve for height or width, then enter the side you already know.
• Read the result to two decimal places. If the value is not an integer, the exact simplified fraction appears below it.

Simplifying a Ratio with GCD

Simplification means dividing both terms by their greatest common divisor, the largest integer that divides both without a remainder. The calculator uses the Euclidean algorithm: repeatedly replace the larger number with the remainder of the smaller divided into it until the remainder is zero, and the last non-zero value is the GCD. For 1920 and 1080, the sequence runs 1920 mod 1080 = 840, 1080 mod 840 = 240, 840 mod 240 = 120, 240 mod 120 = 0, so the GCD is 120 and the simplified ratio is 16:9. Because GCD only exists for integers, this mode requires positive whole numbers; decimals, zero, and negatives raise an error.

Solving a Missing Side

Solve mode treats the ratio as a proportion. If the ratio is rw:rh and you know the width, the height is width × rh ÷ rw. If you know the height, the width is height × rw ÷ rh. The ratio terms may be decimals, such as 1.5:1, and the known side may be any positive number. The preset buttons simply fill the two ratio fields with 16:9, 4:3, 1:1, 21:9, 9:16, or 3:2.

Worked Examples

Identify a resolution. Enter 1440 and 1080 in Simplify Ratio. Both divide by 360, giving 4:3 and a decimal of 1.333:1. The same resolution in 1920 by 1080 gives 16:9 and 1.778:1.

Match a height at 16:9. In Solve Dimension with a 16:9 ratio, solving for height from a width of 1920 returns 1080.00 exactly. Change the width to 1000 and the result is 562.50, with the exact fraction 1125/2 shown below.

Build an ultrawide canvas. Choose the 21:9 preset, solve for width, and enter a height of 1080. The width is 1080 × 21 ÷ 9 = 2520.00. This is the standard 2560-by-1080-class ultrawide shape expressed against a 1080-pixel height.

Common Aspect Ratios at a Glance

Ratio	Decimal	Typical use
1:1	1.000	Square social posts and avatars
4:3	1.333	Older monitors, tablets, presentation slides
3:2	1.500	35 mm photography, many laptop screens
16:9	1.778	HDTV, 1080p and 4K video, most web video
21:9	2.333	Cinema and ultrawide monitors
9:16	0.5625	Vertical phone video and stories

Edge Cases and Limits

The two modes validate differently, which is the most common source of confusion. Simplify Ratio insists on positive integers, because a ratio such as 16.5:9 has no integer GCD. Solve Dimension accepts any positive values but requires both ratio terms to be greater than zero, so a zero term disables the result. Results in Solve mode are rounded to two decimals; when the underlying number is not an integer, the exact fraction is the way to recover full precision. Orientation is easy to reverse by accident: 9:16 is the vertical portrait form of the same sensor as 16:9, so check which term comes first before cropping or resizing. Finally, simplifying is a purely mathematical reduction and does not tell you whether two resolutions share the same physical shape if one has been letterboxed or stretched.

Resizing Without Distortion

The point of a ratio is that scaling both sides by the same factor leaves the shape unchanged. If you know the target width, the correct height is width × rh ÷ rw, and if you know the target height, the correct width is height × rw ÷ rh. Solving one side from the other is what prevents the stretched, squashed look that comes from setting both dimensions independently. For video, keep the source ratio intact and pad the remainder with letterboxing or pillarboxing rather than cropping into the frame. For photos, crop to the target ratio before scaling, so the pixels you keep are the pixels you framed.

Practical Tips

When a result needs to be a whole number of pixels, choose an input that divides evenly: at 16:9, widths divisible by 16 produce integer heights, so 1920 gives 1080 and 1280 gives 720. If the exact fraction is awkward, such as 1125/2, you can round up to 563 and accept a sub-pixel stretch, or scale both terms by two to get 2250 by 1125, which preserves the shape exactly. Double-check orientation before you commit, because 9:16 and 16:9 describe the same panel rotated ninety degrees. Finally, remember that a simplified ratio describes shape only; two screens with the same ratio can still have different pixel densities, so use the ratio for layout and the full resolution for quality decisions.

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