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Similarity ratio · side/area/volume

Similarity ratio calculator (side, area, volume)

Convert a similarity ratio m:n into side/perimeter, area, and volume ratios with clear scale factors. Solve unknown values, infer ratios from area or volume via √/∛, and show why squares and cubes appear with 2D/3D visuals.

Everything runs in your browser. Keep the orientation as small : large; inputs accept integers, fractions (p/q), or decimals and are normalized automatically.

How to use (3 steps)

  1. Enter the similarity ratio as small : large (integers, fractions, or decimals are fine).
  2. Pick a mode: explore all ratios, solve an unknown side/area/volume, or infer the similarity ratio from an area/volume ratio with √ / ∛.
  3. Read the ratios, scale factors, visuals, and steps. Copy the URL, LaTeX, or SVG if you need to share or present.

Inputs and mode

You can also paste “m:n” into either box; the tool splits it automatically.

Everything stays on this page—no server sends data; GA/ads are the only external calls. Reduced motion follows your OS setting and the toggle above.

Side / perimeter

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Similarity ratio (small:large)

Area ratio

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Squares the similarity ratio

Volume ratio

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Cubes the similarity ratio

Scale factors

→ -

Back: -

Visuals (2D/3D)

2D similar figures

3D similar solids

Step-by-step log

Share and export

Use these to hand out examples in class or attach to a worksheet.

FAQ

What is the difference between a similarity ratio and a scale factor?

The similarity ratio is always written as small:large and applies to every length. Scale factors are the multipliers: small→large = n/m and large→small = m/n.

Why does the area ratio square the similarity ratio?

Areas scale with length squared. If the side ratio is m:n, multiplying two sides gives m²:n² for area. The 2D visual highlights the square relationship.

Why does the volume ratio cube the similarity ratio?

Volumes scale with three dimensions. Each dimension follows the similarity ratio, so the volume ratio becomes m³:n³. The 3D visual makes the cube explicit.

How do I get the similarity ratio from an area ratio?

Take the square root of both parts. Perfect squares such as 9:16 become 3:4 exactly; otherwise the tool shows an approximate scale with a caution.

How do I infer the similarity ratio from a volume ratio?

Take the cube root of both parts. Ratios like 8:27 give 2:3 exactly; non-perfect cubes fall back to an approximate multiplier.

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