Trig Angle Calculator
Enter one angle and this calculator returns all six trigonometric ratios at once: sine, cosine, tangent, cosecant, secant and cotangent, each to six decimal places. It works in the forward direction only, from an angle to its ratios, and it takes the angle in degrees. Type 30 and you get sin 30° = 0.500000 and the other five ratios beside it, with no side lengths to enter and no triangle to solve.
Degrees only: a radian value entered here is read as degrees, so convert first (degrees = radians × 180 ÷ π). A displayed ∞ means the ratio is undefined at that angle. A displayed −0.000000 means zero, an artifact of floating-point arithmetic.
Quick Answer
Enter 30° and the calculator returns sin 0.500000, cos 0.866025, tan 0.577350, csc 2.000000, sec 1.154701 and cot 1.732051. It converts the angle to radians internally, evaluates sine and cosine, then builds the other four ratios from those two: tan = sin ÷ cos, csc = 1 ÷ sin, sec = 1 ÷ cos and cot = 1 ÷ tan. The angle must be in degrees, and the tool does not work backwards from a ratio to an angle.
Key takeaways
- This is a forward calculator: one angle in, six ratios out. It does not find unknown angles from side lengths or from ratio values.
- The angle input is degrees only. A radian value typed in is read as degrees, so convert first: degrees = radians × 180 ÷ π.
- A displayed ∞ means the ratio is undefined at that angle, not that it equals a huge number. Tan and sec are undefined at 90° and 270°; csc and cot are undefined at 0° and 180°.
- Negative angles and angles above 360° work, because every ratio repeats every full turn: 390° gives exactly the same six values as 30°.
- Quick Answer
- How to use the trig angle calculator
- The six ratios, and how they are built from two numbers
- Worked example: 30 degrees, checked against the tool
- Where the ratios break down, and what ∞ really means
- Degrees only, and how to handle radians or the reverse question
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the trig angle calculator
Type one number, in degrees, and click Calculate. The results stay hidden until you calculate, so nothing is shown for the pre-filled 30° until you press the button.
- Enter the angle in degrees: the box is pre-filled with 30. Replace it with any angle, including negatives and values above 360.
- Click Calculate: all six ratios appear to six decimal places, in the order sin, cos, tan, csc, sec, cot.
- Read ∞ as undefined: where a ratio has no value, the calculator shows ∞ instead of an error or a giant number.
- Copy or share the result with the buttons in the results box when you want to keep the six values together.
A blank or non-numeric entry is rejected with the message “Please enter a valid angle” and no ratios are shown. Reset restores the worked example value of 30 and hides the results.
The six ratios, and how they are built from two numbers
Only two values are ever computed directly: sine and cosine of the angle. Every other ratio is derived from them, which is why the six outputs always agree with each other. In a right triangle, sine is opposite over hypotenuse, cosine is adjacent over hypotenuse and tangent is opposite over adjacent; on the unit circle the same three are the y-coordinate, the x-coordinate and y over x.
cos θ = adjacent ÷ hypotenuse
tan θ = sin θ ÷ cos θ
csc θ = 1 ÷ sin θ sec θ = 1 ÷ cos θ cot θ = 1 ÷ tan θ
radians = degrees × π ÷ 180 (the conversion the calculator applies before evaluating anything)
The reciprocal names follow the pairing: cosecant inverts sine, secant inverts cosine and cotangent inverts tangent. That pairing is also what decides where each ratio breaks down. A reciprocal of zero does not exist, so csc fails wherever sin is zero and sec fails wherever cos is zero, and the calculator shows ∞ at exactly those angles.
Worked example: 30 degrees, checked against the tool
The calculator is pre-filled with 30, the classic 30-60-90 triangle angle, so the worked example is one click away. The exact values are sin 30° = 1/2, cos 30° = √3/2 and tan 30° = 1/√3, and the tool’s six-decimal output matches those fractions rounded: 0.500000, 0.866025 and 0.577350. The reciprocals follow by inversion: csc 30° = 2, sec 30° = 2/√3 = 1.154701 and cot 30° = √3 = 1.732051.
Every row of the special-angles table below is a real run of this calculator, so you can type any of these angles in and get the same figures back. The 0° and 90° rows are the ones students most often get wrong by hand, because they are where the undefined ratios live.
| Angle | sin | cos | tan | csc | sec | cot |
|---|---|---|---|---|---|---|
| 0° | 0.000000 | 1.000000 | 0.000000 | ∞ | 1.000000 | ∞ |
| 30° | 0.500000 | 0.866025 | 0.577350 | 2.000000 | 1.154701 | 1.732051 |
| 45° | 0.707107 | 0.707107 | 1.000000 | 1.414214 | 1.414214 | 1.000000 |
| 60° | 0.866025 | 0.500000 | 1.732051 | 1.154701 | 2.000000 | 0.577350 |
| 90° | 1.000000 | 0.000000 | ∞ | 1.000000 | ∞ | 0.000000 |
Where the ratios break down, and what ∞ really means
Strictly, tan 90° is undefined, not infinite: cos 90° is zero, and division by zero has no value. The calculator shows ∞ as its display convention for “no value here”, which is honest as a display choice but should not be quoted as a number in homework. The same convention covers sec at 90° and 270°, where cos is zero, and csc and cot at 0° and 180°, where sin is zero.
Two display quirks deserve a sentence each, because they look like errors and are not. At 90°, cot shows 0.000000, which is correct: cot is cos over sin, and 0 over 1 is 0. At 180° and 360°, the tool shows −0.000000 for tangent and sine, which is floating-point arithmetic producing a negative zero; it means exactly zero. Neither quirk changes any other output.
Degrees only, and how to handle radians or the reverse question
This calculator has one unit and one direction, and both limits are stated on the tool itself rather than hidden in fine print. The input is degrees only: there is no radians switch, so a radian value typed in is silently read as degrees and gives a wrong answer that looks plausible. Convert first with degrees = radians × 180 ÷ π. The common conversions are π/6 radians = 30°, π/4 = 45°, π/3 = 60° and π/2 = 90°.
The reverse question, finding an angle from a known ratio, is a different tool entirely. If you know that sin θ = 0.5 and want θ = 30°, use the inverse sine calculator or the inverse cosine calculator instead of this page. If you only need one ratio rather than all six, the cosine calculator gives it on its own. For the 45-45-90 triangle behind the 45° row, the 45-45-90 triangle calculator solves the sides as well as the angles.
What competing calculators miss
Most rival trig tools do the same core job, so the differences are in scope, units and honesty about undefined values:
- Single-ratio tools (including the common sine-only and cosine-only pages): fine when you need one value, but they force six separate runs for a full set, and nothing checks that the six answers agree with each other. This page computes all six from the same two numbers, so they always do.
- All-six tools with a radians switch: genuinely more flexible on units than this page, which is degrees only. The trade is that several of them bury the unit choice in a dropdown that is easy to leave on the wrong setting, and a wrong-unit answer looks just as clean as a right one. This page trades that flexibility for one unambiguous unit, stated in the label.
- All-six tools that print “Undefined”: the more careful display choice, and this page’s ∞ is its equivalent. Where rivals fall down is printing an enormous number instead, such as a 16-digit tangent at 90°, which invites students to copy a meaningless figure into their working.
- Triangle solvers dressed as trig calculators: several pages titled as trigonometry calculators actually solve triangles from sides, or mix triangle solving with ratio evaluation. That is a useful tool, but it is not this one, and a student who only wants six ratios should not have to enter side lengths to get them.
- The gap this page fills: all six ratios from one angle in one click, six-decimal output, an explicit undefined convention, and a degrees-only label that cannot be misread, plus the special-angles table above for checking answers by hand.
Frequently asked questions
It takes one angle in degrees and returns all six trigonometric ratios: sine, cosine, tangent, cosecant, secant and cotangent, each to six decimal places. Enter 30 and you get sin 0.500000, cos 0.866025, tan 0.577350, csc 2.000000, sec 1.154701 and cot 1.732051.
No. This calculator works forward only, from an angle to its ratios. Finding an angle from a known ratio needs an inverse trigonometric function, which this tool does not compute. For that job, use the inverse sine calculator or the inverse cosine calculator.
The ∞ symbol is the calculator’s display for a ratio that is undefined at that angle. Tangent and secant are undefined at 90 degrees and 270 degrees, where cosine is zero, and cosecant and cotangent are undefined at 0 degrees and 180 degrees, where sine is zero. Strictly the value does not exist; ∞ is a display convention, not a number to copy into your working.
No, this calculator accepts degrees only, and a radian value typed in is read as degrees. Convert first with degrees = radians × 180 ÷ π. For example, π/6 radians is 30 degrees, π/4 radians is 45 degrees and π/2 radians is 90 degrees.
Yes. Trigonometric ratios repeat every full turn, so negative angles and angles above 360 degrees give the same values as their position within one turn. Entering 390 degrees gives exactly the same six ratios as 30 degrees, and entering −30 degrees flips the sign of sine, tangent, cosecant and cotangent while cosine and secant stay the same.
That is floating-point arithmetic producing a negative zero, and it means exactly zero. The sine of 180 degrees is zero, and the tangent of 180 degrees is zero, so −0.000000 is the tool’s way of printing zero after its internal radian conversion. It does not affect any other output.
Sine, cosine and tangent are the three primary ratios, and the other three are their reciprocals: cosecant is 1 over sine, secant is 1 over cosine and cotangent is 1 over tangent. Many formulas in physics and engineering are written in terms of secant or cosecant, so having all six in one place saves a round of manual inversion.
Yes. It runs entirely in your browser, needs no account, and stores nothing. Copy the result with “Copy my results” or send it to another app with “Share results”.
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References
- OpenStax, Precalculus 2e. Right Triangle Trigonometry (sine, cosine and tangent as side ratios, SOH-CAH-TOA, reciprocals). Accessed October 24, 2026.
- OpenStax, Precalculus. The Other Trigonometric Functions (tangent as y over x, secant, cotangent and cosecant as reciprocals, domain restrictions). Accessed October 24, 2026.
- Khan Academy. Trigonometric ratios in right triangles (definitions of sine, cosine and tangent, SOH-CAH-TOA worked examples). Accessed October 24, 2026.
- OpenStax, Precalculus 1e via LibreTexts. Unit Circle: Sine and Cosine Functions (unit-circle coordinates as cosine and sine, radian measure). Accessed October 24, 2026.
- Colorado Community Colleges Online, Trigonometry. Finding Trigonometric Functions Using the Unit Circle (unit circle definition, quadrants, x as cosine and y as sine). Accessed October 24, 2026.
- OpenStax, Precalculus 2e. Simplifying and Verifying Trigonometric Identities (even and odd identities, reciprocal identities). Accessed October 24, 2026.