Enter two angles with their units. For more angles, open More angles and enter one number and unit per line, such as 30 deg or -0.5 rad. Get the full signed sum in radians and degrees, plus sine, cosine and tangent.
Angle Addition Formula
Convert angles to a common unit and add them, then evaluate the sine, cosine and tangent of the total. The calculator combines degrees with compensated summation and converts the total to radians.
- \(\theta_{\text{deg}}\) = an angle entered in degrees
- \(\theta_{\text{rad}}\) = the same angle converted to radians
- \(\theta_1, \theta_2, \theta_3, \ldots, \theta_n\) = each angle after conversion to radians if needed
- \(S\) = total angle sum in radians
- \(\sin(S)\) = sine of the total angle
- \(\cos(S)\) = cosine of the total angle
- \(\tan(S)\) = tangent of the total angle
The formulas above express the sum in radians. The calculator uses the equivalent degree sum internally and reports both units, without wrapping the total to one revolution. It also returns sine, cosine and tangent; tangent is undefined at odd multiples of 90°. Each angle and the total must have magnitude at most 1 billion degrees.
Common Angle Conversions and Trig Values
Use these values to check common results when adding angles.
| Degrees | Radians | Decimal Radians |
|---|---|---|
| 0° | 0 | 0.0000 |
| 30° | π/6 | 0.5236 |
| 45° | π/4 | 0.7854 |
| 60° | π/3 | 1.0472 |
| 90° | π/2 | 1.5708 |
| 180° | π | 3.1416 |
| 360° | 2π | 6.2832 |
| Total Angle | Radians | sin | cos | tan |
|---|---|---|---|---|
| 30° | 0.5236 | 0.5000 | 0.8660 | 0.5774 |
| 45° | 0.7854 | 0.7071 | 0.7071 | 1.0000 |
| 90° | 1.5708 | 1.0000 | 0.0000 | Undefined |
| 180° | 3.1416 | 0.0000 | -1.0000 | 0.0000 |
Example Section
Example 1: Add two angles in degrees
Add 30° and 45°.
The angle sum is 1.3090 radians. The trig values are approximately sin(S) = 0.9659, cos(S) = 0.2588, and tan(S) = 3.7321.
Example 2: Add one degree angle and one radian angle
Add 90° and 0.5 radians.
The angle sum is 2.0708 radians. The trig values are approximately sin(S) = 0.8776, cos(S) = -0.4794, and tan(S) = -1.8305.
FAQ Section
Can you add angles measured in degrees and radians together?
Yes. Select the unit beside each of the first two angles. For additional angles, include deg, ° or rad on each line. The calculator converts to a common unit before addition.
Why is the angle sum shown in radians?
Radians are the standard unit used by most trigonometric calculations. This calculator displays the sum in radians as the primary answer and also shows the sum in degrees.
Why can tangent be very large or undefined?
Tangent is calculated as sin(S) divided by cos(S). When cos(S) is very close to 0, tangent becomes very large. At angles such as π/2 radians, or 90°, tangent is undefined because division by zero is not possible.
