Weather & Calamities
Intermediate

Beaufort Wind Scale

Converts a Beaufort force number into an approximate wind speed.

Formula

v=0.836 B3/2v = 0.836\,B^{3/2}

Variables

vWind speed (m/s)
BBeaufort number (0–12)

Example

Force 8 gale: v ≈ 0.836×8^1.5 ≈ 18.9 m/s

How it works

The Beaufort Wind Scale gives a quick way to estimate wind speed from an observed force number based on how the wind affects the environment, such as smoke, leaves, trees, and waves. The formula v = 0.836B^(3/2) is an empirical fit, meaning it was chosen to match observed average wind speeds to Beaufort numbers rather than derived from a fundamental physical law. It is useful because it turns a qualitative weather observation into an approximate speed in metres per second.

When to use it

Use this formula when you have a Beaufort force number and need an approximate wind speed for weather reports, field observations, or classroom exercises. It is especially helpful when converting historical or human-observed wind descriptions into numerical values.

Worked example, step by step

Suppose the wind is rated Beaufort 5. Substitute B = 5 into the formula: v = 0.836 × 5^(3/2) Calculate 5^(3/2) = 5 × √5 ≈ 5 × 2.236 = 11.18 Now multiply: v ≈ 0.836 × 11.18 ≈ 9.35 m/s Final answer: the wind speed is about 9.4 m/s

Common mistakes to avoid

  • Using the wrong exponent, such as squaring B instead of raising it to 3/2
  • Forgetting that the result is in m/s, not km/h or mph
  • Applying the formula to values outside the Beaufort range of 0 to 12

Did You Know?

Admiral Beaufort devised his scale in 1805 to standardise ship logbook wind reports.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026