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Trigonometry Calculator

Evaluate sine, cosine, tangent and their inverses in degrees or radians, and solve a right triangle's missing sides and angles from any two known values.

FreeNo sign-upPrivate — runs in your browser, nothing is uploaded

Trig function evaluator

sin(30°) = 0.5

Right triangle solver

Right angle at C. Enter any two values — at least one side. Leave the rest blank. (a is opposite angle A, b opposite B, c is the hypotenuse.)

a = 3, b = 4, c = 5

Angle A = 36.87° · Angle B = 53.13° · Area = 6

Quick answer

Trigonometry relates the angles of a triangle to the lengths of its sides. This calculator does two jobs: it evaluates the six trig functions (sin, cos, tan, csc, sec, cot) and their inverses for any angle in degrees or radians, and it solves a right triangle — given any two values (with at least one side) it finds the remaining sides, both acute angles, and the area using the Pythagorean theorem and SOH-CAH-TOA.

Formula & method

The function evaluator converts the angle to radians when needed and applies the standard trig functions; inverse functions return an angle in your chosen unit. The right-triangle solver assumes the right angle is at C and applies SOH-CAH-TOA (sin A = opposite/hypotenuse, etc.) together with the Pythagorean theorem a² + b² = c². The two acute angles always sum to 90°, and the area is ½ · a · b.

Examples

Example 1: Evaluate sin 30°
Input
sin, 30, degrees
Result
0.5
Why
The sine of 30° is exactly 0.5 — one of the standard reference angles.
Example 2: Solve a 3-4 right triangle
Input
a = 3, b = 4 (find the rest)
Result
c = 5, A = 36.87°, B = 53.13°
Why
c = √(3² + 4²) = 5; A = atan(3/4) = 36.87°; B = 90° − A = 53.13°.
Example 3: Inverse tangent
Input
arctan, 1, degrees
Result
45°
Why
tan 45° = 1, so arctan(1) = 45° (or π/4 radians).

When to use this tool

  • Checking trig homework or finding an exact function value for a reference angle.
  • Finding a missing side or angle of a right triangle in construction, surveying, or physics.
  • Converting between degrees and radians while evaluating a function.

Common mistakes

  • Leaving the calculator in the wrong angle mode — entering degrees while it expects radians (or vice-versa) is the most common trig error.
  • Forgetting that the hypotenuse is always the longest side of a right triangle and must be opposite the right angle.
  • Trying to solve a triangle from two angles alone — without at least one side length the triangle's size is undetermined.

Frequently asked questions

Does it work in degrees and radians?

Yes. Use the angle-unit selector to switch between degrees and radians; it applies to the input angle for direct functions and to the output angle for inverse functions.

What's the minimum I need to solve a right triangle?

Any two values, as long as at least one is a side length. Two sides, or one side plus an acute angle, are enough; two angles alone are not.

Why does tan 90° show 'undefined'?

Tangent is the ratio sin/cos, and cos 90° = 0, so tan 90° is undefined (it heads to infinity). The tool reports 'undefined' instead of a misleading huge number.

Which angle is A and which is B?

The right angle is at C. Angle A is opposite side a, and angle B is opposite side b, so A and B are the two acute angles that add up to 90°.

Can it give csc, sec, and cot?

Yes — the function list includes cosecant, secant, and cotangent, which are the reciprocals of sine, cosine, and tangent.

Is anything uploaded?

No. All calculations run in your browser.

Sources & references

External references open in a new tab. We are independent and not affiliated with these organizations.

  • ✓ Free to use
  • ✓ No sign-up required
  • ✓ Runs entirely in your browser — nothing is uploaded.
  • ✓ Formula and method shown above
Last updated: How we calculateReport a correctionDisclaimer

Provided “as is” for general information only — results may be inaccurate, so verify before you rely on them. No warranty; use at your own risk.

Built and reviewed by HIFreeTools against the formula shown above and any authoritative references cited on this page. See our methodology and editorial standards.

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