Gradians to Milliradians Converter
Enter a value to instantly convert between angle units.
1 Gradian = 15.708 Milliradian
Key Formulas
Degree → Radian
rad = ° × 0.0174533Radian → Degree
° = rad × 57.2958Degree → Gradian
grad = ° × 1.11111Gradian → Degree
° = grad × 0.9Formula
mrad = gradians × (π × 5)In regions where surveyors work in gradians and military forces use mrad-calibrated optics, joint operations — mapping a firing range, surveying a border corridor, establishing a geodetic reference for an artillery battery — require converting between the two systems. A survey bearing in grad must become milliradians to enter a fire-control computer. The conversion also appears in robotics when servo angle outputs from European engineering software (in grad) must feed a targeting or aiming controller that expects mrad.
Source: ISO 80000-3:2019 (Quantities and units — Space and time)
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Frequently Asked Questions
Real-World Examples
One gradian — 15.708 mrad (= 0.9° = π/200 radians). The conversion anchor for gradian-to-mrad work.
1 grad = 15.708 mrad
A right angle (100 grad) — 1,570.8 mrad = π/2 × 1,000, confirming the 90° angle in both gradian and mrad notation.
100 grad = 1570.8 mrad
100 milliradians back-converted — 6.366 grad, used to verify a mrad-based angular measurement against a gradian-calibrated instrument.
6.366 grad = 100 mrad
A 10 grad survey bearing — 157.08 mrad, entered into a mrad-based fire control system for range and azimuth calculations.
10 grad = 157.08 mrad