Tangent To A Circle Calculator

Work out tangent to a circle instantly with clear inputs, formula shown and shareable results.

About Tangent To A Circle Calculator

A tangent meets the radius at 90°, so the centre, the point of tangency and the external point form a right triangle. The tangent length is therefore √(d² − r²), and both tangents from an external point are equal.

Formulas

Tangent length

t = √(d² − r²)

Half-angle at the point

sin(θ/2) = r / d

Worked example

With the default values below, Tangent To A Circle Calculator returns Tangent length of 12.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Circle radiusminimum 0: 5
Distance from centre to the external pointminimum 0: 13

Results

Tangent length: 12.0000
Angle between the two tangents: 45.2397 °
Angle subtended at the centre: 134.7603 °
Area of the tangent kite: 60.0000

Step by step

1Values used
2Tangent length
3Half-angle at the point
4Tangent length= 12.0000
5Angle between the two tangents= 45.2397 °
6Angle subtended at the centre= 134.7603 °
7Area of the tangent kite= 60.0000

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 4 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

Radius 5, distance 13?

√(169 − 25) = 12, the classic 5-12-13 triple.

What happens when d = r?

The point is on the circle, the tangent length collapses to zero and only one tangent exists.