Geometry GlanceSources

Triangle calculator

cm

cm

Distance to the base line, not a sloping side.

Advanced

Changing a measurement unit keeps its number: 3 cm becomes 3 m. Unit for all measurements applies to every input and the result. Result unit converts only the answers.

Height is perpendicular to the base line. Three sides must form a non-flat triangle.

Number format

Use a decimal point or comma, without thousands separators. Up to 15 significant digits and 64 characters; no fractions or expressions.

Triangle schematic. Height is perpendicular to the base line. Three sides must form a non-flat triangle.bceh

Not to scale

Enter your measurements to see the results.

No personal result is available. These are the triangle formulas and conditions.

Formulas and conditions

Triangle

An obtuse triangle with base b and sides c and e. Dashed height h runs from the opposite vertex perpendicular to the extended base, with its foot outside the triangle and a right-angle mark.bceh
Area
A=bh2
Perimeter
P=b+c+e

b base · c, e other sides · h perpendicular height · q half the perimeter · A area · P perimeter

h > 0; its foot may lie on the extended base. Each side < the sum of the other two.

A sloping side is not h. Base and height alone do not determine perimeter.

Diagrams are schematic, not to scale.

Choose Base and height when you know a base and the perpendicular distance from the opposite vertex to its line. The height may meet the extended base outside an obtuse triangle. These two measurements determine area, but not perimeter.

Choose Three sides when all side lengths are known. Every side must be shorter than the other two added together; 1, 2 and 3 cannot form a non-flat triangle. Heron’s formula gives area, then h = 2A/b gives the height for the side labelled b.

Half perimeter
q=b+c+e2
Heron’s area
A=q(q−b)(q−c)(q−e)
Height for base b
h=2Ab

Use the same length unit throughout a formula. Convert mixed measurements first. Length and perimeter use units such as cm; area uses cm²; volume uses cm³. Decimal examples below are rounded to at most six significant figures, with ≈ marking an approximation.

Worked example: Three sides: 8 cm, 5 cm and 5 cm

  1. P = 8 + 5 + 5 = 18 cm; q = 18 ÷ 2 = 9 cm.
  2. A = √(9 × 1 × 4 × 4) = 12 cm².
  3. h = 2 × 12 ÷ 8 = 3 cm.

The height bisects the 8 cm base into 4 cm halves. Each half forms a 3–4–5 right triangle. Using the 5 cm sloping side as height would wrongly give 20 cm².

Formula sources

Formulas are checked against these references. The explanation, diagrams and worked calculations here are authored for Geometry Glance.