Convert triangle angles between degrees, radians, and gradians. Enter any combination of angle units, verify the angle sum equals 180°, and see all three angles in every unit system with visual pro...
Angles can be measured in degrees, radians, or gradians, and each unit system appears in different contexts. Degrees are the standard in everyday geometry and construction, radians dominate calculus and physics, and gradians (also called gons) are still used in some European surveying traditions where a right angle equals 100 grad.
This triangle degree converter lets you enter the three angles of a triangle in any combination of units — for example, angle A in degrees, angle B in radians, and angle C in gradians — and instantly converts every angle to all three systems. It verifies that the sum equals 180° (π radians, 200 grad) and flags invalid triangles.
The output cards show each angle in degrees, radians, and gradians side by side. Proportion bars visualize how each angle compares to the full 180°. A quick-reference conversion table covers common angles (30°, 45°, 60°, 90°, etc.) so you don't have to memorize formulas. Preset buttons load standard triangles like equilateral, 30-60-90, and right isosceles, making it easy to explore conversions without manual entry. Whether you are a student switching between textbook conventions or a surveyor translating field data, this calculator saves time and prevents errors.
This calculator is useful when triangle work moves between unit systems. It lets you mix degrees, radians, and gradians in a single problem, then confirms whether the converted angles still describe a valid triangle. That is helpful in trigonometry classes, survey notes, programming work, and any workflow where one source uses decimal grads while another uses degree or radian notation.
Degrees → Radians: rad = deg × π/180. Degrees → Gradians: grad = deg × 200/180. Radians → Degrees: deg = rad × 180/π. Gradians → Degrees: deg = grad × 180/200.
Result: Angles convert to 30°, 60°, and 90°, so the triangle is valid
Angle A is 0.523599 rad, which is about 30°. Angle B is already 60°, and angle C is 100 grad, which equals 90°. The converted sum is 180°, so the calculator identifies a valid 30-60-90 triangle and shows each angle in all three unit systems.
Triangle problems do not always arrive in one neat unit system. A textbook may state one angle in degrees, a calculus exercise may express another as a radian multiple of π, and a surveying source may use gradians. Converting everything into a common view before doing any geometry is the safest approach, and that is exactly what this calculator automates.
A conversion is only useful if the triangle still makes sense after the units are standardized. Once all three angles are translated into degrees, the key check is whether they total 180°. If they do not, the issue is often a wrong unit selection, a rounding slip, or data copied from a non-triangular context. The validity card in this tool helps catch those mistakes early.
Gradians are less common in school geometry, but they still appear in surveying and some engineering references because a right angle becomes a clean 100 grad. When you need to compare those values with trigonometric formulas or classroom problems written in degrees and radians, fast conversion prevents avoidable transcription errors. That is why a triangle-specific converter is more useful than a generic unit tool here.
Degrees (360° in a full turn), radians (2π in a full turn), and gradians (400 grad in a full turn). Use this as a practical reminder before finalizing the result.
Multiply the degree value by π/180. For example, 45° × π/180 = π/4 ≈ 0.7854 radians.
Gradians (gons) are used in some European surveying and civil engineering fields where a right angle equals exactly 100 grad. Keep this note short and outcome-focused for reuse.
For a valid triangle: 180° in degrees, π radians, or 200 gradians. Apply this check where your workflow is most sensitive.
Yes. Each angle has its own unit selector, so you can enter Angle A in degrees, Angle B in radians, and Angle C in gradians.
The three angles, once converted to degrees, must add up to approximately 180°. If the sum is significantly different, the triangle cannot exist.