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Triangle Angle Calculator

MathTriangles and Trigonometry
What you know
Angle C (degrees) —
Angle A (°)
—
Angle B (°)
—
Angle C (°)
—
Triangle type
—
Angles in radians
—

A triangle's interior angles always add to 180°, so the third angle is 180° minus the two you know: with 50° and 60°, the missing angle is 70°. If you only have the three side lengths, the law of cosines gives each angle; sides 3, 4 and 5 produce 36.87°, 53.13° and 90°.

About this tool

Geometry students, carpenters checking a roof pitch and anyone laying out a triangular plot often know part of a triangle and need the rest of its angles. This calculator works two ways. Give it two angles and it subtracts them from 180°. Give it three side lengths and it applies the law of cosines to every corner, then reports each angle in degrees and radians and names the triangle as acute, right or obtuse, and as scalene, isosceles or equilateral. It also rejects side sets that cannot close into a triangle. One limit: it does not handle the side-angle-side or side-side-angle cases, so with a mix of sides and angles you will need a law of sines solver.

How to use it

  1. Pick what you know

    Choose Two angles or Three sides at the top; only the matching fields are shown.

  2. Enter the values

    Type angles in degrees, or the three side lengths in any one unit. Each side is labelled by the angle it faces.

  3. Read the angles

    Angle C is the headline figure; A, B, the radian values and the triangle type sit beneath it, with the working shown.

Examples

Sides 3, 4 and 5

What you know
Three sides
Side a (opposite A)
3
Side b (opposite B)
4
Side c (opposite C)
5

Result Angle C (degrees): 90
Angle A (°): 36.87
Angle B (°): 53.13
Angle C (°): 90
Triangle type: Right scalene
Angles in radians: A 0.6435, B 0.9273, C 1.5708

  1. cos A = (b² + c² − a²) ÷ 2bc = (16 + 25 − 9) ÷ 40 = 0.8 → A = 36.87°
  2. cos B = (a² + c² − b²) ÷ 2ac = 0.6 → B = 53.13°
  3. C = 180° − 36.87° − 53.13° = 90°

Because 9 + 16 = 25, the law of cosines returns exactly 90° opposite the longest side, with 36.87° and 53.13° at the other corners.

Angles 50° and 60°

What you know
Two angles
Angle A
50
Angle B
60

Result Angle C (degrees): 70
Angle A (°): 50
Angle B (°): 60
Angle C (°): 70
Triangle type: Acute scalene
Angles in radians: A 0.8727, B 1.0472, C 1.2217

  1. A + B + C = 180°
  2. C = 180° − 50° − 60° = 70°

Subtracting both from 180° leaves 70°; every angle is under 90°, so the triangle is acute.

Angles 30° and 30°

What you know
Two angles
Angle A
30
Angle B
30

Result Angle C (degrees): 120
Angle A (°): 30
Angle B (°): 30
Angle C (°): 120
Triangle type: Obtuse isosceles
Angles in radians: A 0.5236, B 0.5236, C 2.0944

  1. A + B + C = 180°
  2. C = 180° − 30° − 30° = 120°

Two equal base angles of 30° leave a 120° apex, which makes the triangle obtuse and isosceles.

How it is calculated

C = 180° − A − B; cos A = (b² + c² − a²) ÷ (2bc)

A, B, C
interior angles in degrees
a, b, c
side lengths, each opposite the angle with the same letter

With two angles known, the angle-sum theorem fixes the third. With three sides, the law of cosines is solved for angles A and B with the inverse cosine, and C is taken as 180° minus both so the three always total exactly 180°. Side units cancel out, so centimetres, feet or plain numbers all give the same angles. A right triangle is flagged when the largest angle is 90° to within rounding error.

When not to use it

  • You know two sides and an angle; that needs the law of sines or a full triangle solver.
  • You are working on a sphere, such as long-distance navigation, where angles sum to more than 180°.

Common mistakes

  • Matching a side to the wrong angle; side a must face angle A.
  • Entering an exterior angle instead of the interior one.
  • Mixing units across the three sides, such as two in feet and one in inches.

Frequently asked questions

Why do the angles of a triangle add up to 180°?

In flat (Euclidean) geometry, a line through one corner parallel to the opposite side creates alternate angles equal to the other two corners. Together with the corner angle they form a straight line, which is 180°. Euclid proved this as Proposition 32 of Book I.

Can I find the angles from the sides alone?

Yes. Three sides fix a triangle completely, so the law of cosines recovers every angle. For sides 3, 4 and 5 the angles are 36.87°, 53.13° and 90°. The size of the triangle does not matter: sides 6, 8 and 10 give the same angles.

Why are my three sides rejected?

Any side must be shorter than the other two combined, the triangle inequality. Sides 1, 2 and 5 fail because 1 + 2 is less than 5; the two short sides cannot reach each other. If two sides add up exactly to the third, the shape collapses into a flat line and is rejected too.

How is the triangle type decided?

By its largest angle: under 90° is acute, exactly 90° is right, over 90° is obtuse. Separately, three equal angles make it equilateral, two equal angles isosceles, and none equal scalene. The two labels are combined, as in Right scalene or Obtuse isosceles.

Can a triangle have two right angles?

Not on a flat surface. Two 90° angles already total 180°, leaving nothing for the third corner, so the calculator reports an error when angles A and B reach 180° together.

How do I convert the angles to radians?

Multiply degrees by π ÷ 180. A 90° angle is about 1.5708 radians and 60° is about 1.0472. The results list each angle in radians to four decimal places alongside the degree values.

Cite this tool

Using this tool in an assignment, article or report? Copy a citation, or a link for your website.

APA

Tools Directory Editorial Team. (2026, October 13). Triangle Angle Calculator. Tools Directory. Retrieved October 25, 2026, from https://tools.milunir.com/math/triangles-and-trigonometry/triangle-angle-calculator/

MLA

Tools Directory Editorial Team. “Triangle Angle Calculator.” Tools Directory, 13 Oct. 2026, https://tools.milunir.com/math/triangles-and-trigonometry/triangle-angle-calculator/. Accessed 25 Oct. 2026.

Chicago

Tools Directory Editorial Team. “Triangle Angle Calculator.” Tools Directory. Last modified October 13, 2026. Accessed October 25, 2026. https://tools.milunir.com/math/triangles-and-trigonometry/triangle-angle-calculator/.

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