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Calculators / Math / Circle chord from centre distance
Circle chord from centre distance calculator
Find the length of a circle chord from its perpendicular distance to the centre.
On this page
Chord length8units
Minor central angle106.26degrees
Calculator controls
How to calculate
Find the length of a circle chord from its perpendicular distance to the centre.
Chord length =
2*sqrt(R^2-d^2) unitsMinor central angle =
2*acos(d/R)*180/pi degreesWorked example
- Circle radius: 5
- Centre-to-chord distance: 3
- Chord length: 8 units
- Minor central angle: 106.26 degrees
Assumptions and limits
All lengths must use one common unit. These are ideal geometric measurements; allowances, thickness, manufacturing tolerances and measurement uncertainty are excluded. The centre-to-chord distance cannot exceed the radius.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Find the length of a circle chord from its perpendicular distance to the centre. The distance must be perpendicular to the chord. A zero distance gives the full diameter.
When this tool is useful
The distance must be perpendicular to the chord. A zero distance gives the full diameter.
Understanding your inputs
| Input | Example |
|---|---|
Circle radius R | 5 |
Centre-to-chord distance d | 3 |
Frequently asked questions
Which assumptions matter for this result?
All lengths must use one common unit. These are ideal geometric measurements; allowances, thickness, manufacturing tolerances and measurement uncertainty are excluded. The centre-to-chord distance cannot exceed the radius.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.