Triangle Calculator

Euclidean Triangle Geometry & Trigonometric Standards

A valid Euclidean triangle must satisfy the Triangle Inequality Theorem, stating that the sum of the lengths of any two sides must be strictly greater than the third side: a + b > c.

Primary Triangle Equations

• Semi-Perimeter (s): s = (a + b + c) / (2)

• Heron's Area Formula:

Area = √(s(s - a)(s - b)(s - c))

• Law of Cosines for Interior Angles:

α = ((180^) / (π))

β = ((180^) / (π))

γ = 180^ - α - β

• Inradius (r): r = Areas

• Circumradius (R): R = (a × b × c) / (4 × Area)

• Altitudes: h_a = 2 × Areaa, h_b = 2 × Areab, h_c = 2 × Areac

How to Use This Calculator

Enter your Side a Length (e.g. 6), Side b Length (e.g. 8), Side c Length (e.g. 10), and Measurement Unit — choose from Centimeters (cm), Meters (m), Inches (in). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Formula Reference: Triangle Calculator

Input variables:

sideALength — Side a Length

sideBLength — Side b Length

sideCLength — Side c Length

unitOfMeasurement — Measurement Unit

Computed outputs:

triangleArea — Triangle Area (Heron's Formula)

trianglePerimeter — Total Perimeter

angleAlphaDegrees — Angle α (Opposite a)

angleBetaDegrees — Angle β (Opposite b)

angleGammaDegrees — Angle γ (Opposite c)

Mathematical relationships extracted from calculation logic:

perimeter = a + b + c

s = perimeter / 2

cosAlpha = Math.max(-1, Math.min(1, (b b + c c - a a) / (2 b * c)))

cosBeta = Math.max(-1, Math.min(1, (a a + c c - b b) / (2 a * c)))

alphaDeg = alphaRad * (180 / Math.PI)

betaDeg = betaRad * (180 / Math.PI)

gammaDeg = 180 - alphaDeg - betaDeg

circumradius = safeDiv(a b c, 4 * area)

Standard: NIST / ISO mathematical definitions

Worked Example

A triangular roof truss with side lengths of 6 ft, 8 ft, and 10 ft encloses an area of 24 sq ft, creates a perfect 90° right angle at the apex, and requires 24 linear feet of framing lumber.

Understanding Your Result

Geometric calculations assume ideal shapes — real-world measurements should include a 5–15% tolerance for irregular shapes, cutting waste, and installation overlap. For construction applications: always verify calculated areas match your physical measurements before ordering materials. Standard practice is to measure the same dimension twice from different reference points and use the average. Express results in the units required by your supplier or building permit — conversions between cubic yards, cubic feet, and cubic meters must be precise for material orders.