Gradians to Turns Converter
Enter a value to instantly convert between angle units.
1 Gradian = 0.0025 Turn
Key Formulas
Degree → Radian
rad = ° × 0.0174533Radian → Degree
° = rad × 57.2958Degree → Gradian
grad = ° × 1.11111Gradian → Degree
° = grad × 0.9Formula
turns = gradians ÷ 400Automation systems and robotics controllers often express rotation limits in turns (full revolutions), while surveying instruments in gradian mode output grad. When a gradian-mode total station is integrated with an automated scanning platform — a robotic total station, a lidar turret — the angular position reported in grad must be converted to turns for the motor controller's position API. Animated simulations of surveying traverses also need this conversion to drive rotation keyframes.
Source: ISO 80000-3:2019 (Quantities and units — Space and time)
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Frequently Asked Questions
Real-World Examples
Full circle (400 grad) — 1 turn, confirming the instrument completes exactly one revolution in gradian mode.
400 grad = 1 tr
A right angle (100 grad) — 0.25 turns (quarter revolution), the position a robotic arm must reach to orient 90° from its start.
100 grad = 0.25 tr
A straight-line bearing (200 grad = 180°) — 0.5 turns, the half-revolution position for a scanning turret's U-turn.
200 grad = 0.5 tr
A 50 grad rotation (45°) — 0.125 turns (one-eighth revolution), the eighth-turn keyframe in a rotation animation.
50 grad = 0.125 tr