Chord Length Calculator
A chord joins the two ends of an arc. At 180° it equals the diameter, and the height shown is the maximum gap between arc and chord.
Your numbers
Chord length
28.284cm
Arc length
31.416cm
Height
5.858cm
Formula
Chord length = 2 × Radius × sin(Angle (°) ÷ 2)
A chord is always shorter than its arc — the gap between them tells you how sharp the curve is.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Radius (cm)Centre to edge — half the diameter. | 20 | 0 and up |
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 90 | 0 ~ 360 |
Step by step
Quick reference table
Results when only Radius (cm) changes and everything else stays put.
| Radius (cm) | Chord length (cm) | Arc length (cm) | Height (cm) |
|---|---|---|---|
| 10 | 14.142 | 15.708 | 2.929 |
| 15 | 21.213 | 23.562 | 4.393 |
| 20 | 28.284 | 31.416 | 5.858 |
| 30 | 42.426 | 47.124 | 8.787 |
| 40 | 56.569 | 62.832 | 11.716 |
What each result means
| Result | At default values |
|---|---|
| Chord length (cm)The straight line between two points on a circle. | 28.284 |
| Arc length (cm)The length of the curved piece cut from a circle’s edge. | 31.416 |
| Height (cm)The perpendicular height from the base — not the slanted side. | 5.858 |
Common mistakes
A chord is always shorter than its arc — the gap between them tells you how sharp the curve is.
Glossary
- Radius
- Centre to edge — half the diameter.
- Angle (°)
- An angle in degrees; a full turn is 360°.
- Chord length
- The straight line between two points on a circle.
- Arc length
- The length of the curved piece cut from a circle’s edge.
- Height
- The perpendicular height from the base — not the slanted side.
Frequently asked questions
Q. How is Chord Length Calculator calculated?
Chord length = 2 × Radius × sin(Angle (°) ÷ 2) — A chord joins the two ends of an arc. At 180° it equals the diameter, and the height shown is the maximum gap between arc and chord.
Q. Can you walk through an example?
With Radius 20cm, Angle (°) 90°, the answer is Chord length 28.284cm.
Q. What do I need to enter?
Enter Radius, Angle (°). The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Radius (cm) moves the answer to Radius (cm) 10 → Chord length (cm) 14.142 and Radius (cm) 40 → Chord length (cm) 56.569. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
A chord is always shorter than its arc — the gap between them tells you how sharp the curve is.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.