Gradians to Radians Converter
Enter a value to instantly convert between angle units.
1 Gradian = 0.0157 Radian
Key Formulas
Degree → Radian
rad = ° × 0.0174533Radian → Degree
° = rad × 57.2958Degree → Gradian
grad = ° × 1.11111Gradian → Degree
° = grad × 0.9Formula
radians = gradians × (π ÷ 200)Surveying instruments in gradian mode produce measurements in grad that must enter trigonometric formulas, GIS coordinate calculations, or physics models that all work in radians. A traverse calculation that computes a closing error vector, or a geodetic adjustment that minimizes least-squares residuals, requires that all input angles be in radians before the formulas can execute. Every European survey bearing in grad needs this conversion before going into the math.
Source: ISO 80000-3:2019 (Quantities and units — Space and time)
Last reviewed: · see our methodology
Frequently Asked Questions
Real-World Examples
A right angle on the total station (100 grad) — converts to π/2 ≈ 1.5708 radians, the value passed to the atan2() function in a coordinate transformation.
100 grad = 1.5708 rad
A 50 grad diagonal bearing — π/4 ≈ 0.785 radians, confirming a 45° line in a geometric construction calculation.
50 grad = 0.7854 rad
A back-bearing (200 grad) — π ≈ 3.1416 radians, the opposite direction in a reverse-bearing traverse check.
200 grad = 3.1416 rad
Full circle (400 grad) — 2π ≈ 6.2832 radians. Verifying the instrument completes a full 2π radian circuit in gradian mode.
400 grad = 6.2832 rad