Triangle Calculator

Knowing a triangle's full geometry from partial information is a common task in construction, surveying, and geometry class. The law of cosines extends the Pythagorean theorem to any triangle, not just right triangles. Give it two sides and the angle between them (SAS), or all three sides (SSS), and the full picture follows. For SAS, the law of cosines computes the missing side, then the law of sines fills in the remaining angles. Area is simply half the product of the two known sides and the sine of the included angle. For SSS, the same law works in reverse: each angle is found by rearranging the equation. The triangle type classification uses the largest angle. If it equals 90 degrees, the triangle is right. Less than 90 is acute, greater than 90 is obtuse.

• Land surveying: Surveyors often measure two sides and the angle between them. Entering those three values gives the full parcel dimensions without extra fieldwork.
• Construction and carpentry: Cutting rafters or bracing requires knowing all angles. Start from the known dimensions and use SAS or SSS to confirm every angle before cutting.
• Geometry homework: Verify law of cosines and Heron's formula results instantly. Enter your given values and check each step of the worked output against your own work.
• Navigation and mapping: GPS-based distance calculations between three points reduce to triangle problems. SSS mode handles any such configuration and returns all bearings.

1. 1Select SAS (two sides, one angle) or SSS (three sides) from the calculation type.
2. 2For SAS, enter sides a and b and the angle C between them in degrees.
3. 3For SSS, enter all three sides a, b, and c.
4. 4The calculator applies the law of cosines to find any unknown sides or angles.
5. 5Area is computed using the sine formula (SAS) or Heron's formula (SSS).
6. 6The triangle is classified as right, acute, or obtuse based on the largest angle.

• Entering the wrong angle for SAS: Angle C must be the angle between sides a and b, not an angle opposite one of them. Entering the wrong angle produces a valid but incorrect result with no error message.
• Using degrees when the formula expects radians: This calculator accepts degrees and converts internally. If you are checking the result by hand, remember to convert your angle to radians before applying cos or sin.
• Ignoring the triangle inequality for SSS: Three positive numbers do not always form a triangle. If a + b is not greater than c (for any permutation), no real triangle exists. The calculator flags this as an error.
• Confusing area with perimeter: Area is in square units. Perimeter is in the same units as the sides. If sides are in meters, area is in m² and perimeter is in m. The calculator returns raw numbers, so unit tracking is up to you.

• Use SAS for construction problems: If you know two lengths and the angle between them, SAS is always available from a single measurement setup. SSS requires all three lengths, which sometimes needs an extra measurement.
• Check right-angle problems with the Pythagorean shortcut: For a 90-degree included angle, cos(90°) = 0 so the law of cosines becomes a² + b² = c². You can verify the result by checking that the two shorter sides satisfy the Pythagorean theorem.
• Confirm triangle type before fabricating parts: The triangle-type field tells you right, acute, or obtuse at a glance. An unexpected obtuse result from a supposed right-angle joint means your angle measurement is off.
• Scale inputs proportionally to preserve shape: To find angles for a similar triangle of different size, multiply all sides by the same factor. Angles do not change when sides scale uniformly.