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Angular Unit Converter

Convert between degrees, radians, milliradians, microradians, arc-minutes, and arc-seconds. Calculate beam spread at a distance.

Angular quantities in photonics and beam characterization appear in six common units depending on context: degrees for large rotation angles and goniometer settings, radians for analytical computation, milliradians (mrad) for beam divergence and pointing stability, microradians (µrad) for fine alignment tolerances, arc-minutes for angular apertures, and arc-seconds for astronomical and autocollimator specifications. This converter accepts any angle in any of these units and returns all six equivalents simultaneously. A secondary beam-spread panel computes lateral growth — radius and diameter — at a user-specified propagation distance for either the full divergence angle or the half-angle, useful for estimating spot size at a target or detector at distance.

Angle Input
mrad
Beam Divergence Utility
Angular Conversions
Degrees (°)
0.06875°
Radians
0.00120rad
Milliradians
1.2000mrad
Microradians
1200.0µrad
Arc-minutes (′)
4.1253
Arc-seconds (″)
247.5
Beam Spread at 10 m
Radius growth (from full-angle divergence)
r = d × tan(θ_half)
6.0000mm
Diameter growth
Full beam spread = 2 × radius growth
12.000mm
Add your initial beam diameter to the diameter growth to get total beam size at the target distance. For Gaussian beams, this is approximate — the exact calculation requires beam waist and Rayleigh range.
Abridged Optics — Angular Unit Converter v1.01 rad = 206,265 arc-seconds. For beam displacement, solid angle, and error propagation calculations, see the Optical Geometry Calculator.

All information, equations, and calculations have been compiled and verified to the best of our ability. For mission-critical applications, we recommend independent verification of all values. If you find an error, please let us know.