Advanced Geometry Estimator

Triangle Calculator Online: Sides, Angles, Area & Trigonometry

A powerful triangle calculator to instantly solve for unknown side lengths, angles, perimeter, and area. Utilize our right triangle calculator mode to automatically find the hypotenuse alongside sin, cos, and tan trigonometry ratios.

Primary Result: Triangle Area - Enter values to calculate triangle properties.

Right Triangle Calculator (90°)

Solve for the hypotenuse, angles, and trigonometry ratios.

Two Legs (a, b) Leg & Hypotenuse (a, c) Leg & Angle A (a, A°)

Leg a (Opposite to A)

Leg b (Adjacent to A)

Leg a (Opposite to A)

Hypotenuse c

Leg a (Opposite to A)

Angle A (Degrees)

Hypotenuse c-

Leg a / Leg b-

Angle A / Angle B-

Perimeter-

sin(A) / cos(A) / tan(A)-

Side-Side-Side (SSS) Calculator

Calculate angles and area when all three side lengths are known.

Side a

Side b

Side c

Angle A-

Angle B-

Angle C-

Perimeter-

Semi-perimeter (s)-

Side-Angle-Side (SAS) Calculator

Calculate missing values given two sides and the included angle.

Side a

Angle C (Degrees)

Side b

Side c-

Angle A-

Angle B-

Perimeter-

Angle-Side-Angle (ASA) Calculator

Calculate missing values given two angles and the included side.

Angle A (Degrees)

Side c (Between A & B)

Angle B (Degrees)

Angle C-

Side a-

Side b-

Perimeter-

Calculation Settings

Decimal Places

Triangle Formulas & Trigonometry Mathematics

Understanding the backend geometry formulas helps verify your manual calculations against our triangle calculator.

Pythagorean Theorem (Right Triangle)

Used to find the hypotenuse (c) or missing leg of a right triangle when two sides are known.

a² + b² = c²

Basic Trigonometry (SOH CAH TOA)

Relates the angles of a right triangle to the ratios of its side lengths.

sin(A) = opp/hyp | cos(A) = adj/hyp

Law of Cosines (SAS & SSS)

Used to find a missing side when two sides and the included angle are known, or to find angles when all sides are known.

c² = a² + b² - 2ab · cos(C)

Heron's Formula (Area from SSS)

Calculates the area of any triangle given all three side lengths. 's' is the semi-perimeter.

Area = √(s(s-a)(s-b)(s-c))

Geometry & Trigonometry FAQ

How do I calculate the hypotenuse of a right triangle?

Using the Pythagorean theorem (a² + b² = c²), square the lengths of the two smaller sides (legs), add them together, and then find the square root of that sum to get the hypotenuse length (c).

What do SSS, SAS, and ASA mean?

These are congruency postulates determining what information is known about a triangle. SSS (Side-Side-Side) means you know all three lengths. SAS (Side-Angle-Side) means you know two sides and the angle between them. ASA (Angle-Side-Angle) means you know two angles and the side connecting them.

How does the sine cosine tangent calculator work?

In a right triangle, Trigonometric ratios compare the lengths of specific sides. Sine (sin) is the Opposite side divided by the Hypotenuse. Cosine (cos) is the Adjacent side divided by the Hypotenuse. Tangent (tan) is Opposite divided by Adjacent.

Can any three lengths form a valid triangle?

No. According to the Triangle Inequality Theorem, the sum of the lengths of any two sides must be strictly greater than the length of the remaining third side (a + b > c). Our SSS calculator automatically checks this rule.