Angle Converter

What is an Angle Conversion Calculator?

An angle conversion calculator lets you convert angles between units such as degrees (°), radians (rad), gradians (gon), or milradians (mils). People use these units in mathematics, physics, engineering, and navigation.

Why do We Need to Convert Angles?

Different fields use angle units for different reasons:

Degrees: Used in daily life and geometry.

Radians: Used in mathematics and trigonometry.

Gradians: Used in surveying and engineering.

Angle conversion helps keep calculations accurate and ensures that formulas and actual measurements work correctly.

How to Convert Angle Units

You can change angle units using a conversion factor. Once you know the factor, the multiplication is easy:

S × C = E

Where S is the starting number, C is the factor, and E is the answer.

For example, to convert any unit to degrees, take 5 radians and multiply by the factor from the table.

5 radians × 57.29578 [degrees / radians] = 286.4789 degrees

To convert degrees in the left column back to units, divide by the number in the right column, or multiply by its inverse (1/x).

286.4789 degrees ÷ 57.29578 [degrees / radians] = 5 radians

To go between any two units in the left column, say A to B, first convert A to degrees by multiplying it by its factor, then dividing by the factor of B to get the new unit. Or, you can just take the factor of A and divide it by the factor of B to get a straight number.

For example, to convert radians to rotations, multiply by 57.29578 and then divide by 360. Or, use 57.29578 ÷ 360 = 0.1591549. So, to go from radians to rotations directly, you would multiply by 0.1591549.

Now see how the units cancel out. Suppose you want to convert radians to degrees. Since multiplying by 1 does not change the value but does change the unit, set it so that “radians” cancel out and “degrees” remain.

Because:

1 degree = 0.01745329 radians, so 1 degree ÷ 0.01745329 radians = 1

We write it this way:

1 radian = 1 radian × (1 degree ÷ 0.01745329 radians) = 57.29578 degrees

So the factor to convert radians to degrees is 57.29578 because 1 × 57.29578 = 57.29578. Note that there is a small rounding here.

Now, since 1 radian = 57.29578 degrees, we can reverse it. Divide both sides by 57.29578 and you get approximately 0.01745329 radians = 1 degree. Therefore, the factor to convert degrees back to radians is approximately 0.01745329.

Radians to Degrees

Radians to degrees is a way to change the unit of an angle in geometry. We measure angles in two systems, called radians and degrees. Radians are used mostly in trigonometry. To change an angle from radians to degrees, we use a formula. To learn this, we will first see the meaning of each unit of angle. We will also look at a table that shows radians to degrees conversion.

Radians to Degrees Conversion

We measure angles in two units: radians and degrees. So, it is important to know how to change one unit into the other. When we take the radius of a circle and turn it, we form an angle. That angle can be written in radians or degrees. Let us now see what these two units mean and how to measure them.

Radians

When we move the radius one full round of the circle, it makes one complete rotation. The angle formed at the center after one full turn is 2π radians. In radians, the angle is the ratio of arc length to radius length. If the arc length is equal to the radius length, the angle formed at the center is 1 radian. We write this unit as rad. Radian is the SI unit for measuring angles.

Degrees

Angles can also be measured in degrees. One full circle is divided into 360 equal parts, and each part is one degree. After one complete turn of the radius, the angle formed at the center is 360°. The symbol for degree is “°”. Degrees are not an SI unit, but they are still widely used. That is why we often convert radians into degrees while solving problems. We use a protractor to measure angles in degrees.

If we compare both units for one complete rotation, we get:

360° = 2π radians

180° = π radians

Radians to Degrees Formula

We use the radians to degrees formula to change radians into degrees. To do this, we multiply the value in radians by 180°/π. Angles can be written in degrees or radians. One degree is written as 1°, and one radian is written as 1 rad. If an angle is written without a unit, it means it is in radians. One full circle is 360° in degrees and 2π in radians. This shows how degrees and radians are related.

The formula is:

Angle in Radians × 180°/π = Angle in Degrees

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