Calculating your arc length is straightforward once you know the Arc Length formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Arc Length Calculator.
What is Arc Length?
The Arc Length calculation tells you your arc length from a few simple inputs. The figure you are solving for here is the arc length.
The Arc Length formula
The core formula is:
Arc length = 2 × 3.141592653589793 × Radius × Central angle ÷ 360Here is what each input means:
- Radius — a value measured in units. Example: 6 units.
- Central angle — a value measured in degrees. Example: 90 degrees.
How to calculate it step by step
- Write down the radius (for example, 6 units).
- Write down the central angle (for example, 90 degrees).
- Apply the formula above to get your arc length.
- Double-check the result with the Arc Length Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Radius | 6 units |
| Central angle | 90 degrees |
| Arc length | 9.4248 |
With radius of 6 units and central angle of 90 degrees, the arc length works out to 9.4248.
Example 2
With radius of 12 units and central angle of 90 degrees, the arc length works out to 18.8496.
| Result | Value |
|---|---|
| Arc length | 18.8496 |
Example 3
With radius of 3 units and central angle of 90 degrees, the arc length works out to 4.7124.
| Result | Value |
|---|---|
| Arc length | 4.7124 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Arc Length Calculator does it instantly, for free, with the formula and a worked example built in.
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