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 = product of the two angles, in squared units such as ยฐยฒ or radยฒ
- A1 = angle 1
- A2 = angle 2
If the product and one angle are known, the missing angle is found by division.
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.
- Product mode: select Product, then enter angle 1 and angle 2. The calculator multiplies the two angles.
- Angle 1 mode: select Angle 1, then enter angle 2 and the product. The calculator divides the product by angle 2.
- Angle 2 mode: select Angle 2, then enter angle 1 and the product. 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 / ฯ degrees | 57.2958ยฐ |
| 1 degree | ฯ / 180 radians | 0.0174533 rad |
| 1 radยฒ | (180 / ฯ)ยฒ degreesยฒ | 3282.8064 ยฐยฒ |
| 1 degreeยฒ | (ฯ / 180)ยฒ radiansยฒ | 0.000304617 radยฒ |
Common Angle Products
| Angle 1 | Angle 2 | Product |
|---|---|---|
| 30ยฐ | 45ยฐ | 1350 ยฐยฒ |
| 60ยฐ | 90ยฐ | 5400 ยฐยฒ |
| ฯ/6 rad | ฯ/3 rad | ฯยฒ/18 radยฒ, about 0.5483 radยฒ |
| 0.5 rad | 2 rad | 1 radยฒ |
Examples
Example 1: Find the product in degrees squared
Suppose angle 1 is 25ยฐ and angle 2 is 40ยฐ.
The product is 1000 ยฐยฒ.
Example 2: Find a missing angle
Suppose the product is 1800 ยฐยฒ and angle 1 is 30ยฐ. To find angle 2, divide the product by angle 1.
The missing angle is 60ยฐ.
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 ยฐยฒ. Radians times radians gives radians squared, written as radยฒ.
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 canโt the known angle be zero when finding a missing angle?
To find a unique missing angle, the known angle must be nonzero. If the known angle and product are both zero, any missing angle works. If the known angle is zero but the product is not, there is no solution.
