Angle & Solid Angle Converter

Overview

Plane Angles measure flat rotation: • degree (°), radian (rad), grad (gon), mil (NATO, Swedish, Warsaw), • arcminute (′), arcsecond (″).
Solid Angles measure space angle: • steradian (sr), square degree (deg²), spat (sphere).

Formula & Methodology

Convert via SI pivot for plane: \( θ_{\!rad} = θ_{\text{input}} × f_{\text{from}} \), \( θ_{\text{out}} = θ_{\!rad} / f_{\text{to}} \). For solid: \( Ω_{\!sr} = Ω_{\text{input}} × f_{\text{from}} \), \( Ω_{\text{out}} = Ω_{\!sr} / f_{\text{to}} \).

Examples

• 45° → rad: 45×π/180 = 0.785398 rad
• 1 mil (NATO) → °: (2π/6400)×180/π ≈ 0.05625°
• 2 sr → deg²: 2×(180/π)² ≈ 6573.0 deg²

Use Cases

• Artillery: mils for targeting.
• Surveying: grads for civil engineering.
• 3D graphics: steradians for light probes.

Frequently Asked Questions