Use the free Trigonometry Calculator below: your data never leaves your browser — all work happens on your device, and nothing is uploaded to any server.
What Trigonometry Actually Measures
Trigonometry is the study of triangles, and more exactly of the ratios that stay the same no matter how big a triangle is. Take any right triangle with a 30-degree angle. The side opposite that angle is always half the hypotenuse, whether the triangle is drawn on paper or is a roof ten metres wide. That fixed ratio is the sine of 30 degrees, and it equals 0.5. Once you know that ratios like this are fixed, you can work out unknown lengths and angles from the few numbers you do know, which is why trigonometry is used in building, surveying, navigation, and games.
The three main ratios are sine, cosine, and tangent. In a right triangle, sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. A simple memory aid is SOH-CAH-TOA: Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent. If you can remember those three lines, you can set up almost any basic trigonometry problem, and this calculator does the arithmetic for you.
How to Use This Calculator
Enter an angle and choose degrees or radians, then press Calculate sin, cos, tan. The tool shows all three values, the angle in both units, and a check that sin squared plus cos squared equals 1. That check is not decoration: it is a built-in proof that the answers are consistent, because the identity sin² + cos² = 1 holds for every angle. If you enter 90 degrees, you will see that tangent is undefined, because cosine is zero there and dividing by zero is not allowed.
For the inverse side, enter a value and press Calculate inverses. Arcsin answers the question: which angle has this sine? Arccos and arctan do the same for cosine and tangent. Note the limits: arcsin and arccos only accept values from -1 to 1, because no sine or cosine can be larger than 1 or smaller than -1. Arctan accepts any value, and the tool shows it alongside the others whenever the input is valid.
A Worked Example: A Ramp and a Tree
Suppose a ramp rises at 30 degrees and its sloped length is 10 metres. How high is the top? The height is the side opposite the angle, so height = 10 × sin(30°) = 10 × 0.5 = 5 metres. Try 30 in the tool and you will see sin = 0.5, which confirms the step. Now suppose you stand 20 metres from a tree and the angle to its top is 45 degrees. The height is 20 × tan(45°) = 20 × 1 = 20 metres. Tangent is the right ratio here because you know the adjacent side and want the opposite side.
An inverse example: a ladder leans against a wall, and the ratio of height to ladder length is 0.8. Which angle does the ladder make with the ground? That is arcsin(0.8), about 53.13 degrees. Enter 0.8 in the inverse section and check: arcsin gives about 53.13, and sin(53.13°) returns 0.8. Going forwards and backwards like this is the best way to build trust in the tool.
Degrees and Radians, Explained Simply
Degrees split a full circle into 360 parts, which is convenient for everyday use. Radians measure an angle by the arc length it cuts on a circle of radius 1, so a full circle is 2π radians, about 6.283. Radians feel strange at first, but they make calculus and physics formulas much simpler, which is why science and engineering use them. The conversion is simple: radians = degrees × π ÷ 180, and degrees = radians × 180 ÷ π. This calculator converts for you, so you can enter either unit and read both.
A common mistake is mixing the two units: entering 30 expecting degrees while the tool is set to radians, or the reverse. Always glance at the unit selector before you calculate. Another common mistake is using the wrong ratio, for example sine when the problem gives the adjacent side. Sketch the triangle, label opposite, adjacent, and hypotenuse for your angle, and the right ratio usually becomes clear.
Try It Yourself
Start with the famous angles: 0, 30, 45, 60, and 90 degrees. Memorising their sines and cosines pays off, because they appear in exams again and again. Then try an inverse: enter 0.5 and confirm arcsin is 30 degrees. Finally, solve a real problem from your own life, such as the height of a shelf, the slope of a ramp, or the angle of a ladder. Every calculation runs in your browser, and nothing you type is sent anywhere.