The calculation, without hidden assumptions
Angle units serve different jobs: degrees are familiar in everyday geometry, radians are natural for mathematics and programming, gradians appear in surveying, and arcminutes/arcseconds provide fine angular subdivisions for navigation and astronomy. MAXScanner keeps them on one canonical converter, shows every equivalent together and preserves the exact circle relationship 360° = 2π rad = 400 grad = 1 turn rather than presenting radians as an arbitrary decimal factor.
How to use this calculator
Enter the angle and choose its source unit. Negative angles and angles greater than one full turn remain valid numerical inputs.
Select the target unit and use the all-equivalent panel to compare degrees, radians, gradians, turns and angular subdivisions.
Treat coordinate DMS strings such as 51°30′26″ as a separate formatting/parsing task; this converter works on one numeric angular quantity at a time.
Where people use it
- •Trigonometry and programming
- •Surveying and CAD
- •Navigation and astronomy angle checks
- •Converting fine angular tolerances and instrument specifications
Example: 180 degrees to radians
180° × π/180 equals exactly π radians, approximately 3.14159265 rad. It is also 200 gradians and one-half turn.
What the result does not assume
- •Degrees-minutes-seconds coordinates and bearings contain multiple fields/sign conventions and are not parsed as one number here.
- •Displayed decimal radians are approximations of relationships that may be exact in terms of π.
Frequently asked questions
How many radians are in 180 degrees?+
Exactly π radians.
How many gradians are in 90 degrees?+
A right angle is exactly 100 gradians because a full turn is 400 gradians.
What is an arcminute?+
One arcminute is 1/60 of a degree; one arcsecond is 1/60 of an arcminute or 1/3,600 of a degree.
Can angles be negative?+
Yes. A sign can represent rotational direction or orientation under the convention being used.
Semantic next steps
Continue the calculation
These links move to a different input, formula or project stage rather than a keyword variation of this page.
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Keep the result connected to the real job
MAXScanner keeps the formula and assumptions beside the result so you can verify the number before using it in a drawing, estimate, specification, worksheet or document. Where a supplier, manufacturer, drawing or applicable standard owns a requirement, that source remains authoritative.