Everyday Math
Basic

Aspect Ratio Scaling

Find a height that preserves an aspect ratio.

Formula

h=w×rhrwh = w \times \frac{r_h}{r_w}

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Variables

wWidth
r_h,r_wRatio terms

Example

1920 wide at 16:9 = 1080 tall

How it works

Aspect ratio tells you how width and height should compare so an image or shape does not look stretched. If the ratio is given as width:height = r_w:r_h, then keeping that same proportion means the height must scale by the same factor as the width, which gives h = w × (r_h / r_w). This is just proportional reasoning: multiply the width by the height-to-width fraction of the ratio.

When to use it

Use this when resizing photos, videos, screens, posters, or any rectangular object while keeping its shape unchanged. It is also useful in design and printing when you know one side and need the matching side from a fixed ratio.

Worked example, step by step

A poster is 50 cm wide and must keep a 5:4 aspect ratio. Use h = w × (r_h / r_w) Substitute the values: h = 50 × (4 / 5) Compute the fraction: 4 / 5 = 0.8 Multiply: h = 50 × 0.8 = 40 Final answer: the height should be 40 cm

Common mistakes to avoid

  • swapping the ratio terms and using rw/rh instead of rh/rw
  • using the wrong side as the starting value, such as treating height like width
  • forgetting that the ratio must stay in the same order as written

Did You Know?

16:9 is the standard for modern screens and video.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026