Calculate the missing value in an angle multiplication problem by entering two angles or a product in degrees, radians, or squared units.
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Angle Multiplication Formula
The angle multiplication calculator uses the basic product formula for two angles. The product has squared angle units, such as degrees squared or radians squared.
P = A_1 * A_2
- P = product of the two angles, in squared units such as °² or rad²
- A1 = angle 1
- A2 = angle 2
If the product and one angle are known, the missing angle is found by division.
A_1 = P / A_2
A_2 = P / A_1
When units are mixed, the calculator converts angles to degrees first, performs the multiplication or division, then converts the answer back to the selected output unit.
degrees = radians * 180/pi
degrees^2 = radians^2 * (180/pi)^2
- Product mode: enter angle 1 and angle 2, then leave the product field empty. The calculator multiplies the two angles.
- Angle 1 mode: enter angle 2 and the product, then leave angle 1 empty. The calculator divides the product by angle 2.
- Angle 2 mode: enter angle 1 and the product, then leave angle 2 empty. The calculator divides the product by angle 1.
- Unit handling: angles can be entered in degrees or radians. Products can be entered or returned in degrees squared or radians squared.
Angle Unit Conversion Values
Use these values to check how degree and radian inputs relate before multiplication.
| Quantity | Equivalent value | Approximate decimal |
|---|---|---|
| 1 radian | 180 / π degrees | 57.2958° |
| 1 degree | π / 180 radians | 0.0174533 rad |
| 1 rad² | (180 / π)² degrees² | 3282.8064 °² |
| 1 degree² | (π / 180)² radians² | 0.000304617 rad² |
Common Angle Products
| Angle 1 | Angle 2 | Product |
|---|---|---|
| 30° | 45° | 1350 °² |
| 60° | 90° | 5400 °² |
| π/6 rad | π/3 rad | π²/18 rad², about 0.5483 rad² |
| 0.5 rad | 2 rad | 1 rad² |
Examples
Example 1: Find the product in degrees squared
Suppose angle 1 is 25° and angle 2 is 40°.
P = 25 * 40
P = 1000 degrees^2
The product is 1000 °².
Example 2: Find a missing angle
Suppose the product is 1800 °² and angle 1 is 30°. To find angle 2, divide the product by angle 1.
A_2 = 1800 / 30
A_2 = 60 degrees
The missing angle is 60°.
FAQ
Why is the product in squared units?
When you multiply one angle by another angle, the units multiply too. Degrees times degrees gives degrees squared, written as °². Radians times radians gives radians squared, written as rad².
Can angle multiplication use negative angles?
Yes. A negative angle multiplied by a positive angle gives a negative product. Two negative angles give a positive product. The calculator follows normal multiplication and division rules for signs.
Why can’t the known angle be zero when finding a missing angle?
To find a missing angle, the calculator divides the product by the known angle. Division by zero is undefined, so the known angle cannot be zero in that case.
