Perpendicular Bisector Calculator

Work out perpendicular bisector instantly with clear inputs, formula shown and shareable results.

About Perpendicular Bisector Calculator

The perpendicular bisector passes through the midpoint of a segment at right angles to it, so its gradient is the negative reciprocal of the segment's. Every point on it is equidistant from the two endpoints.

Formula

Perpendicular bisector

through ((x₁+x₂)/2, (y₁+y₂)/2) with gradient −(x₂−x₁)/(y₂−y₁)

Worked example

With the default values below, Perpendicular Bisector Calculator returns Equation of the perpendicular bisector of y = -1.5x + 10. Change any input above and every figure here is recalculated in your browser.

Inputs used

x₁: 1
y₁: 2
x₂: 7
y₂: 6

Results

Equation of the perpendicular bisector: y = -1.5x + 10
Midpoint it passes through: (4, 4)
Gradient of the bisector: -1.50000000
Length of the segment: 7.21110255

Step by step

1Values used
2Perpendicular bisector
3Equation of the perpendicular bisector= y = -1.5x + 10
4Midpoint it passes through= (4, 4)
5Gradient of the bisector= -1.50000000
6Length of the segment= 7.21110255

Assumptions and limits

The result is derived only from the 4 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 8 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

Bisector of (1,2) to (7,6)?

The midpoint is (4, 4), the segment gradient is 2/3, so the bisector is y = −1.5x + 10.

Why does it matter for circles?

The perpendicular bisectors of a triangle's sides meet at the circumcentre, the centre of the circle through all three vertices.