How to use it
- Enter the angle.
- Choose its unit: degrees, radians, gradians or turns.
- Read the conversions and DMS form.
- Check sin, cos, tan, cot and the angle type.
Angle units
| Unit | Full circle | Right angle |
|---|---|---|
| Degrees (°) | 360° | 90° |
| Radians (rad) | 2π ≈ 6.2832 | π/2 ≈ 1.5708 |
| Gradians (gon) | 400 | 100 |
| Turns | 1 | 0.25 |
Degrees to radians: multiply by π/180. 30° = π/6 ≈ 0.5236 rad. Radians to degrees: multiply by 180/π. 1 rad ≈ 57.2958°.
The calculator converts your angle to all four units at once, normalizes it to 0–360°, names the angle type (acute, right, obtuse and so on) and gives its complement and supplement. Everything runs in your browser.
Sine, cosine, tangent and cotangent
In a right triangle, for an angle θ:
- sin θ = opposite / hypotenuse
- cos θ = adjacent / hypotenuse
- tan θ = opposite / adjacent = sin θ / cos θ
- cot θ = adjacent / opposite = 1 / tan θ
A common memory aid is SOH-CAH-TOA. For angles beyond 90°, the values come from the unit circle and can be negative. Tangent is undefined at 90° and 270°, and cotangent at 0° and 180°; the calculator says "undefined" there instead of showing a huge number.
Exact values of special angles
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 ≈ 0.8660 | √3/3 ≈ 0.5774 |
| 45° | √2/2 ≈ 0.7071 | √2/2 ≈ 0.7071 | 1 |
| 60° | √3/2 ≈ 0.8660 | 1/2 | √3 ≈ 1.7321 |
| 90° | 1 | 0 | undefined |
The calculator shows decimal values rounded to 8 places; teachers often expect the exact forms in this table.
Degrees, minutes and seconds
Latitude, longitude, surveying and astronomy often use degrees, minutes and seconds (DMS): 1° = 60′ and 1′ = 60″.
Example: Seattle's latitude is about 47.6062°. Multiply the decimal part by 60: 0.6062 × 60 = 36.372, so 36′. Multiply the remainder by 60 again: 0.372 × 60 = 22.32″. Result: 47° 36′ 22.32″.
The calculator does this conversion for any angle you enter.
Practical uses
- Roof pitch: a 6-in-12 roof rises 6 inches per 12 inches of run. Its angle is arctan(6/12) ≈ 26.57°, which you can find with the inverse tangent (tan⁻¹) on the scientific calculator, then check here.
- Ramps: the ADA maximum slope for ramps is 1:12, an angle of about 4.76°.
- Programming: most programming languages use radians, so convert degrees before calling sin or cos.
- Navigation: compass bearings are in degrees, often written in DMS.
To solve a whole triangle, use the triangle calculator.
Common mistakes
- Wrong calculator mode. sin(30) is 0.5 in degrees but −0.988 in radians. Always check which unit an angle is in.
- Mixing up complement and supplement. Complementary angles add to 90°, supplementary angles to 180°.
- Treating minutes as decimals. 47° 30′ is 47.5°, not 47.30°.
- Forgetting signs beyond 90°. cos 120° is −0.5; the unit circle sets the sign.
- Negative angles. −30° is the same direction as 330°. The calculator normalizes the angle so you can see its type and position on the circle.
- Rounded special values. 0.8660 is only an approximation of √3/2; write the exact form when a problem asks for it.
All conversions happen in your browser as you type, so you can try several angles quickly and compare their sine, cosine and tangent side by side.
Frequently asked questions
How do I convert degrees to radians?
Multiply by π/180. For example, 90° × π/180 = π/2 ≈ 1.5708 rad.
What is sin 30°?
Exactly 1/2, or 0.5.
Why is tan 90° undefined?
tan θ = sin θ / cos θ, and cos 90° = 0, so the division is undefined.
How do I convert decimal degrees to DMS?
Keep the whole degrees, multiply the decimal part by 60 for minutes, then multiply the remaining decimal by 60 for seconds.
What are gradians?
A unit that divides a full circle into 400 parts, so a right angle is 100 gradians. It is used in some surveying work.
Last updated: November 12, 2026