Triangle Calculator

Calculate all sides, angles, area, and perimeter of a triangle from any 3 known values.
Known Values

Area

17.32

Perimeter

20.00

Type

Scalene / Acute

Sides

Side a5.0000
Side b7.0000
Side c8.0000

Angles

Angle A38.21°
Angle B60.00°
Angle C81.79°
Sum of Angles180.00°

Properties

By SidesScalene
By AnglesAcute
Area17.3205
Perimeter20.0000

Use the Triangle Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only and does not constitute tax, financial, or legal advice. Results are estimates based on the information you provide and current rates. Always consult a qualified tax professional or financial advisor for advice specific to your situation.

How It Works

Our Triangle Calculator is your essential tool for deciphering any triangle's complete geometry. Input just three known values—sides or angles—and instantly receive all missing sides, angles, its area, and perimeter. This is crucial for architects designing the 2026 'Green Tower' with its unique triangular facades, or for surveyors mapping complex 2026 urban development zones.

The calculator employs a combination of trigonometric laws, including the Law of Sines (a/sin A = b/sin B = c/sin C) and the Law of Cosines (c² = a² + b² - 2ab cos C), along with Heron's formula for area when all sides are known, or 0.5 * base * height. It iteratively solves for unknown parameters based on the specific triplet of input values.

Always ensure your angle inputs are consistent (degrees or radians); our calculator defaults to degrees. A common mistake is entering three angles that don't sum to 180 degrees, which will result in an impossible triangle. Remember that two sides and a non-included angle can sometimes lead to two possible triangles (the ambiguous case), which our calculator will highlight.

Example: Calculating a Solar Panel Array for a 2026 Eco-Home

  1. 1 Input: An eco-home roof design requires a triangular solar panel array with two known sides measuring 7.5 meters and 9.0 meters, and the included angle between them is 70 degrees.
  2. 2 Calculation: Using the Law of Cosines, c² = 7.5² + 9.0² - 2 * 7.5 * 9.0 * cos(70°). Then, apply the Law of Sines to find the remaining angles, and finally, Area = 0.5 * 7.5 * 9.0 * sin(70°).
  3. 3 Intermediate Result: The third side (c) is approximately 9.35 meters. The other two angles are approximately 50.3 degrees and 59.7 degrees.
  4. 4 Final Result: The complete solar panel array has sides of 7.5m, 9.0m, and 9.35m. Its angles are 70°, 50.3°, and 59.7°. The total area available for solar cells is approximately 31.72 square meters, and the perimeter requiring sealing is 25.85 meters.

Source: Khan Academy · Last updated: April 2026

Frequently Asked Questions

How do you find the area of a triangle?
The most common formula is area = 1/2 times base times height. If you know all three sides, use Heron formula: area = square root of s(s-a)(s-b)(s-c), where s is the semi-perimeter.
How do you find the missing angle of a triangle?
The three angles of any triangle always add up to 180 degrees. Subtract the two known angles from 180 to find the third. For example, if two angles are 45 and 60, the third is 180 - 45 - 60 = 75 degrees.
What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse (longest side) equals the sum of the squares of the other two sides: a squared plus b squared equals c squared. This only works for right triangles.

You might also need

Percentage Calculator

Calculate percentages three ways: what is X% of Y, X is what % of Y, and percentage change from X to Y.

Fraction Calculator

Add, subtract, multiply, and divide fractions. Results shown as fraction, mixed number, and decimal.

Standard Deviation Calculator

Calculate mean, variance, and standard deviation (population and sample) from a data set.