Angle conversion

Radians to Degrees Converter

Supply an amount measured in radians to find its counterpart in degrees. The page keeps both unit labels visible and checks the answer in the opposite direction.

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 benchmark boxes use the same unit meanings 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 coefficient is 57.295779513082.

Plane angle can be expressed as a fraction of a turn or as an arc-to-radius ratio. If another input defines rad differently, resolve that standard before accepting the ° answer. Keeping those roles distinct prevents an otherwise sound figure from carrying an incorrect 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 audit checks backward instead of rerunning the same arithmetic. 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 paperwork, labels, and systems that expect different units. Record the entered rad amount next to the calculated ° amount.

That pair provides a compact checking record. Should the degrees figure look unusual later, the original radians measurement and the stated coefficient 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 follows unit cancellation rather than memorized direction. Put rad opposite the input's rad label and retain °.

Accuracy and input data for degrees

Round degrees according to the task supported by the measurement. A rough audit and an engineering specification do not usually share one ° accuracy.

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

Carrying the ° answer forward

Save the entered radians measurement with the unrounded degrees output. This brief record enables later reconstruction of radians to degrees without guessing which accuracy was used.

A quick boundary test for Radians to Degrees

Compare the sample answer against an approximate arithmetic based on 57.295779513082 ° per rad.

If the coefficient was inverted, the inverse arithmetic 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 audit the degrees answer?

Run radians to degrees backward using the answer as the input. 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 imply that every ° decimal were measured.

Can I convert negative radians values?

Numerically, yes. Meaning depends on whether the context permits a negative radians can occur in the system being described.