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Free 30-60-90 triangle calculator. Calculate sides, angles, area, and perimeter of 30-60-90 triangles with step-by-step solutions and ratios. Our calculator uses the special right triangle properties to determine all triangle measurements from any given side length.
Last updated: February 2, 2026
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5
opposite 30°
8.660254
opposite 60°
10
opposite 90°
21.650635 square units
23.660254 units
Short : Hypotenuse
1 : 2
Actual: 0.5 : 1
Long : Hypotenuse
√3 : 2
Actual: 0.866025 : 1
Short : Long
1 : √3
Actual: 0.57735 : 1
Side relationships
1 : √3 : 2
Calculates short side, long side, and hypotenuse from any input
Area formula
A = (√3/2) × s²
Uses the special 30-60-90 triangle area formula
Perimeter formula
P = s(3 + √3)
Calculates perimeter from short side length
Triangle type
30°-60°-90°
Special right triangle with unique angle relationships
Key ratios
Short:Long:Hyp = 1:√3:2
Shows fundamental ratios of 30-60-90 triangles
Angles
30°, 60°, 90°
Fixed angle measurements for 30-60-90 triangles
For a 30-60-90 triangle with short side = 5:
Short Side
5
Long Side
8.66
Hypotenuse
10
Our 30-60-90 triangle calculator uses the fundamental properties of special right triangles to calculate all measurements from any given side length. The calculation applies geometric relationships and trigonometric principles to determine sides, angles, area, and perimeter.
Short Side : Long Side : Hypotenuse = 1 : √3 : 2Long Side = Short Side × √3Hypotenuse = Short Side × 2Area = (√3/2) × Short Side²These ratios are fundamental to 30-60-90 triangles and allow calculation of all properties from any single side length. The relationships are based on the geometric properties of equilateral triangles.
Shows the side relationships and angle measurements
The 30-60-90 triangle is derived from an equilateral triangle by drawing an altitude, which creates two congruent 30-60-90 triangles. The side ratios come from the geometric properties of equilateral triangles and the Pythagorean theorem.
Need help with other triangle calculations? Check out our triangle area calculator and hypotenuse calculator.
Get Custom Calculator for Your PlatformResult: Short side = 6, Long side = 10.39, Hypotenuse = 12
Area = 31.18 square units, Perimeter = 28.39 units
Long side = 9√3
Short side = 9, Hypotenuse = 18
Hypotenuse = 14
Short side = 7, Long side = 7√3
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