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Ratio Of Areas And Volumes Calculator

Work out ratio of areas and volumes instantly with clear inputs, formula shown and shareable results.

About Ratio Of Areas And Volumes Calculator

For similar figures a length ratio of k gives an area ratio of k² and a volume ratio of k³. If the material density is unchanged, mass follows volume and also scales by k³.

Formula

Similar figures

lengths : k, areas : k², volumes : k³

Worked example

With the default values below, Ratio Of Areas And Volumes Calculator returns Area ratio of 2.77777778. Change any input above and every figure here is recalculated in your browser.

Inputs used

First linear measurementminimum 0
3
Second linear measurementminimum 0
5

Results

Area ratio
2.77777778
Length ratio
1.66666667
Volume ratio
4.62962963
Mass ratio at equal density
4.62962963

Step by step

  1. 1Values used
  2. 2Similar figures
  3. 3Area ratio= 2.77777778
  4. 4Length ratio= 1.66666667
  5. 5Volume ratio= 4.62962963
  6. 6Mass ratio at equal density= 4.62962963

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Lengths 3 and 5?

The length ratio is 5/3, areas are in the ratio 25/9 ≈ 2.7778 and volumes 125/27 ≈ 4.6296.

Why does this limit how large animals can get?

Bone cross-sectional strength grows as k² while body mass grows as k³, so scaled-up creatures become proportionally weaker.

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