Triangle Altitude Calculator

Work out triangle altitude instantly with clear inputs, formula shown and shareable results.

About Triangle Altitude Calculator

Every altitude satisfies Area = ½ × side × altitude, so once Heron's formula gives the area each altitude follows as hₐ = 2·Area / a.

Formula

Altitude from area

hₐ = 2·Area / a, with Area = √[s(s−a)(s−b)(s−c)]

Worked example

With the default values below, Triangle Altitude Calculator returns Altitude to side a of 8.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Side aminimum 0: 6
Side bminimum 0: 8
Side cminimum 0: 10

Results

Altitude to side a: 8.0000
Altitude to side b: 6.0000
Altitude to side c: 4.8000
Area (Heron): 24.0000

Step by step

1Values used
2Altitude from area
3Altitude to side a= 8.0000
4Altitude to side b= 6.0000
5Altitude to side c= 4.8000
6Area (Heron)= 24.0000

Assumptions and limits

The result is derived only from the 3 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

Can an altitude fall outside the triangle?

Yes. In an obtuse triangle two of the altitudes meet the extensions of the sides rather than the sides themselves.

Which altitude is shortest?

The altitude to the longest side, since the product side × altitude is constant.