Angle conversion

Radians to Degrees Converter

Enter a value in radians to calculate the corresponding amount in degrees. The result updates from the published unit relationship and includes a reverse check so a misplaced factor is easier to spot.

Source measurement

Enter radians

rad

Enter the amount stated in radians.

What this converter answers for Radians to Degrees

A direct radians to degrees answer is useful for geometry, trigonometry, navigation, programming, and technical diagrams.

The entered rad amount and displayed ° amount refer to one unchanged angle measurement.

One conversion shown: rad to °

Set the input to 3.141593 rad. It becomes 180 °, as shown by 3.141593 × 57.295779513082 = 180.

All three tiles preserve the same unit definitions used by radians to degrees.

1.5708 rad90 °
3.1416 rad180 °
7.854 rad450 °

Definitions behind rad and °

The page reserves rad for the entered radians amount and ° for the calculated degrees amount. The fixed factor is 57.295779513082.

Plane angle can be expressed as a fraction of a turn or as an arc-to-radius ratio. If another source defines rad differently, resolve that standard before accepting the ° result. Keeping those roles distinct prevents an otherwise valid number from being assigned to the wrong side of radians to degrees.

The fixed relationship in Radians to Degrees

Treat 57.295779513082 as the scale linking rad with °. Multiply radians by 57.295779513082 to obtain degrees.

Multiply radians by 57.295779513082 to obtain degrees.

A reliable check reverses the operation rather than repeating it. Divide degrees by 57.295779513082 to return to radians.

This page fixes the destination at °; the angle converter handles other targets. Related arithmetic appears in degrees to gradians.

Using degrees in context

Work involving geometry, trigonometry, navigation, programming, and technical diagrams can span forms, labels, and software that expect different units. Record the entered rad amount next to the calculated ° amount.

That pair provides a compact audit trail. Should the degrees value look unusual later, the original radians measurement and the stated factor are still available.

The unit ratio for Radians to Degrees

The one-unit benchmark is 57.2957795131 ° for every rad. Inverse checking relates each ° to 0.0174532925 rad.

A conversion fraction is oriented by its units rather than memory. Put rad opposite the input's rad label and retain °.

Precision and source data for degrees

Round degrees according to the decision the number supports. A rough check and a technical specification rarely need the same ° precision.

The radians to degrees factor is defined more precisely than many real-world radians measurements.

Carrying the ° result forward

Save the entered radians measurement with the unrounded degrees output. This small record lets a later user reproduce radians to degrees without guessing which precision was used.

A quick boundary test for Radians to Degrees

Compare the sample answer with an easy mental estimate based on 57.295779513082 ° per rad.

If the factor was inverted, the reverse calculation will not return 3.141593 rad.

Questions about radians to degrees

What is the formula for radians to degrees?

Multiply radians by 57.295779513082 to obtain degrees. Divide degrees by 57.295779513082 to return to radians.

How can I check the degrees result?

Run radians to degrees backward using the result as the source. Recovering the original rad figure verifies that radians and degrees were not transposed.

Does zero rad equal zero °?

Yes. Zero rad maps to zero ° because radians to degrees has no zero-point offset.

How should degrees be rounded after radians to degrees?

Match degrees to the significant information in radians. A long calculator output should not be copied as though every ° decimal were measured.

Can I convert negative radians values?

Numerically, yes. Context determines whether an amount stated as negative radians can occur in the system being described.