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Accurately convert between 8 angle units including degrees, radians, minutes, seconds, and gradians. Ideal for engineering, math, and surveying.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
Enter a number and choose its unit to see the equivalent angle in degrees, radians, gradians, minutes of arc, and seconds of arc. The value is an angle measure; changing its unit does not change the angle itself. This is a one-value conversion rather than a degrees-minutes-seconds (DMS) parser. The radian is the SI unit for plane angle, and NIST documents the relationship between radians and degrees in its Guide to the SI.
Useful reference relationships are 360° = 2π rad = 400 gradians, and 1° = 60 minutes of arc = 3,600 seconds of arc. Therefore 90° equals 100 gradians, 5,400 arcminutes, or 324,000 arcseconds. A radian conversion uses 180°/π radians per degree; for example, 60° is π/3 radians, approximately 1.0472 rad.
Arcminutes and arcseconds measure subdivisions of an angle. Their marks (′ and ″) can resemble minute and second marks for time, but here they are angular units.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Type a numeric value. Zero, signed values, and fractional values are valid inputs; for example, an orientation offset can be negative.
Select the unit that describes your entered number: degree, radian, gradian, arcminute, or arcsecond. The results show the equivalent in the supported set, including the input unit itself.
Set the displayed precision from 0 to 10 places. Use a practical number of decimal places for your report or next calculation, then copy the needed result from its row.
If you select a result as a new input, the converter switches to that unit and carries on from the displayed rounded value. For calculations where precision matters, enter the original unrounded value again before converting.
Use cases
See how the tool fits into real work and everyday tasks.
If a device reports an angle in radians but your notes use degrees, select radians as the source and read the degree result. Confirm the unit setting before using it in another program.
Convert a known angle such as 60 degrees to radians to see the equivalent fraction π/3 in approximate decimal form. Keep the exact symbolic value separately when a proof requires it.
Surveying, astronomy, or measurement notes may express angles in arcminutes or arcseconds. Select the corresponding angular unit; do not interpret these labels as durations.
Q&A
Find concise answers to common questions and confusing cases.
Multiply degrees by π/180 to get radians, or multiply radians by 180/π to get degrees. For example, 60° = π/3 rad, about 1.0472 rad.
No. Enter one numeric angle value and select one supported unit. To convert DMS first, use decimal degrees: degrees + minutes/60 + seconds/3600, applying the sign to the complete angle. For example, 30° 15′ 10″ is about 30.2528°.
Not in this converter. The minute and second marks here mean 1/60 and 1/3,600 of a degree respectively.
The precision control determines how many decimal places are displayed. The results are rounded for display, so increase the setting if you need more digits or preserve the original input for a high-precision calculation.
Notes
Review scope, result limitations, and important precautions before use.
A numeric conversion cannot determine whether the selected source unit matches your original measurement. Verify the unit label before copying a value into engineering, navigation, or scientific work. The displayed results are rounded to your selected decimal precision; rounding can affect later calculations. DMS notation must be reduced to one decimal angle value before entry, and this converter does not accept a full DMS string.
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