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Gradians to Radians Converter (grad to rad)

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Live Conversion • ISO 80000-3:2019 Certified
1 Gradian = 0.015707963 Radian
1 grad = 0.015708 rad • 1 rad = 63.661977 grad
Gradian to Radian: One Gradian is equal to 0.015707963 Radians.
Certified Authority Value
0.01570796
rad
Exact: 1 rad ≡ 63.6619772368 grad
grad
grad
Swap to Radian to Gradian
Swap to Radian to Gradian
rad
rad 0.015707963
Quick Values:
Conversion Formula
To convert Gradian to Radian, multiply by 0.015707963
grad × 0.015707963 = rad

Calculation: 1 grad × 0.015707963 = 0.015707963 rad

Common Gradian to Radian Calculations

Quick-lookup reference table showing calculated equivalents for standard increments between Gradian (grad) and Radian (rad).

Tap any row to calculate
Gradian to Radian: Primary Direct Table (15 Steps)
Gradian to Radian Conversion Reference Table
Conversion & Equivalent Value Scientific Notation
0.001 grad 1.570796 × 10⁻⁵ rad 1.571 × 10⁻⁵
0.01 grad 0.00015708 rad 1.571 × 10⁻⁴
0.1 grad 0.0015708 rad 1.571 × 10⁻³
0.5 grad 0.00785398 rad 7.854 × 10⁻³
1 grad 0.015708 rad 1.571 × 10⁻²
2 grad 0.0314159 rad 3.142 × 10⁻²
5 grad 0.0785398 rad 7.854 × 10⁻²
10 grad 0.15708 rad 1.571 × 10⁻¹
20 grad 0.314159 rad 3.142 × 10⁻¹
25 grad 0.392699 rad 3.927 × 10⁻¹
50 grad 0.785398 rad 7.854 × 10⁻¹
100 grad 1.570796 rad 1.571 × 10⁰
250 grad 3.926991 rad 3.927 × 10⁰
500 grad 7.853982 rad 7.854 × 10⁰
1000 grad 15.707963 rad 1.571 × 10¹
Radian to Gradian: Reciprocal Summary
Radian to Gradian Conversion Reference Table
Reciprocal & Equivalent Value Scientific Notation
1 rad 63.661977 grad 6.366 × 10¹
5 rad 318.309886 grad 3.183 × 10²
10 rad 636.619772 grad 6.366 × 10²
50 rad 3183.098862 grad 3.183 × 10³
100 rad 6366.197724 grad 6.366 × 10³
View Complete 15-Row Radian to Gradian Table

Real-World Context & Everyday Benchmarks

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To help contextualize these units in everyday life, science, and engineering, here are verified real-world reference points for Gradian (grad) and Radian (rad):

Gradian References:

  • Metric decimal graduation right angle division (100 grad = 90°) 100 grad

Radian References:

  • Subtended angle of arc equal in length to circle radius (~57.3°) 1 rad
  • Complete circular rotation angle expressed in radians (2π rad / 6.283 rad) 6.283 rad

Tap any benchmark above to automatically calculate its exact equivalent in Radian.

ISQ Dimension: Dimensionless [L / L] Coherent SI Unit: radian (rad) Geoscience, Geodesy & Petroleum Engineering

How to Convert Gradian to Radian

Converting Gradian (grad) to Radian (rad) is a core calculation in Plane Angle, which measures the circular arc subtended between two intersecting rays or diverging lines. Because Radian is a broader physical scale than Gradian, converting from grad to rad condenses the numerical figure. It takes 63.661977 Gradian to equal a single Radian (1 grad = 0.015708 rad). To convert any quantity, multiply by 0.015708 (or divide by 63.661977).

Direct Factor1 grad = 0.015708 rad
Inverse Ratio1 rad = 63.661977 grad
Conversion ScaleDirect Proportional Magnitude Compression
First-Principles SI Derivation ProofNIST SP 811 / ISO 80000 Compliance

Mathematical Conversion Derivation via Coherent SI Base Unit

Under the International System of Quantities (ISQ), dimensional conversion between non-SI units is rigorously resolved by bridging through the coherent SI base unit (radian (rad)) without arbitrary rounding:

Vtarget=Vsource×(ksource→SIktarget→SI)V_{\text{target}} = V_{\text{source}} \times \left( \frac{k_{\text{source} \to \text{SI}}}{k_{\text{target} \to \text{SI}}} \right)
Universal Dimensional Conversion Law (ISO 80000 / NIST SP 811)
1. Source SI Bridge (ksource):1 grad = 0.9 radian (rad)
2. Target SI Bridge (ktarget):1 rad = 57.29578 radian (rad)
Step-by-step substitution for Gradian → Radian:V(rad) = V(grad) × ( 0.9 / 57.29578 ) = V(grad) × 0.015708
Mathematical FormulaValue in Radian = Value in Gradian × 0.015707963Direct computational formula applied for standard conversion.
Worked Example

To convert 12 Gradian (grad) to Radian (rad): multiply 12 by 0.015708 to get 0.188496 rad. At an industrial engineering scale, 10000 grad converts to 157.079633 rad.

Inverse check: 1 rad = 63.661977 grad.

Understanding Gradian and Radian

Gradian

grad
Standard Unit

A Gradian (grad) is a recognized unit for plane angle.

Applications & Practical Context

In practical angle terms, a metric decimal graduation right angle division (100 grad = 90°) equals 100 grad.

Physical Setup

A physical magnitude of 1 grad corresponds to 0.9 rad in standard SI measurement.

Conversion to SI Unit: radian (rad)
1 grad = 0.9 rad

Radian

rad
Standard Unit

A Radian (rad) is a recognized unit for plane angle.

Applications & Practical Context

In practical angle terms, a subtended angle of arc equal in length to circle radius (~57.3°) equals 1 rad, a complete circular rotation angle expressed in radians (2π rad / 6.283 rad) equals 6.283 rad.

Physical Setup

A physical magnitude of 1 rad corresponds to 57.29578 rad in standard SI measurement.

Conversion to SI Unit: radian (rad)
1 rad = 57.29578 rad

Domain Metrology & Engineering Applications

Governing Law & Equation

Subtended Circular Arc Ratio (θ = s / r)

Measurement Instrumentation

Rigorously quantified in laboratory and field settings using electronic digital theodolites, optical polygon autocollimators, and rotary optical angle encoders.

Primary Industry Sectors

Applied across geodetic triangulation surveys, aerospace satellite gimbal tracking, civil bridge alignment, and telescope mount tracking under international metrology standard ISO 80000-3:2019.

Physical Orders of Magnitude & Laboratory Reference Benchmarks

Physical Phenomenon / Engineering ReferenceReference ValueConverted to Radian
Subtended angle of arc equal in length to circle radius (~57.3°)1 rad0.015708 rad
Complete circular rotation angle expressed in radians (2π rad / 6.283 rad)6.283 rad0.0986931 rad
Institutional Metrology & Standard Authority:

Formulas, conversion coefficients, and base definitions on this page strictly adhere to the ISO 80000-3:2019 and the BIPM SI Brochure (9th Edition). Governed by Subtended Circular Arc Ratio (θ = s / r) under ISO 80000 dimensional vector Dimensionless [L / L].

Multi-Variable Engineering Bridge Trigonometry & Circular Trajectory

Angular Rotation to Tangential Arc Length Bridge (Meters • Centimeters • Millimeters • Kilometers • Feet • Inches)

Calculate curved perimeter arc length s = r × θ × (π/180) subtended along circular trajectories, bridging angular rotation and travel distance [L] via radius (r).

s = r × θ × (π/180)
Vector: [°] × [π/180 rad/°] × [m] → [m]
Live Calculated Bridge Equivalent:
1 grad at 28" Commuter Bicycle Wheel (0.35 m) = 0.005498 m
Equals 5.4978 × 10⁻⁶ km • 0.5498 cm • 5.4978 mm
SI Length
0.005498
m
Meters
Geographic Scale
5.4978 × 10⁻⁶
km
Kilometers
Engineering Scale
0.5498
cm
Centimeters
Precision Machining
5.4978
mm
Millimeters
US Architectural
0.01804
ft
Feet
US Tooling
0.2164
in
Inches
  1. 1. Normalize Input to SI Base Unit (°):
    θ = 1 grad × 0.9 = 0.9 °
  2. 2. Apply Engineering Parameter (r):
    Selected condition: 28" Commuter Bicycle Wheel (0.35 m) at r = 0.35 m
  3. 3. Execute Governing Physical Law in SI Units:
    s = r × θ × (π/180) = (0.01745 rad/°) × (0.35 m) × (0.9 °) = 0.00549779 m
  4. 4. Convert to Standard Engineering Units:
    • m: 0.00549779 × 1 = 0.005498 m (Meters) • km: 0.00549779 × 0.001 = 5.4978 × 10⁻⁶ km (Kilometers) • cm: 0.00549779 × 100 = 0.5498 cm (Centimeters) • mm: 0.00549779 × 1000 = 5.4978 mm (Millimeters) • ft: 0.00549779 × 3.2808 = 0.01804 ft (Feet) • in: 0.00549779 × 39.3701 = 0.2164 in (Inches)
Explore Arc Length Converter →
Engineering Substance / Operating Standard Parameter Value (m) Reference State / Condition Typical Industrial & Engineering Application
Wall Clock Minute Hand (0.15 m) 0.15 0.15 m (150 mm) Mechanical analog clock tip trajectory radius (15 cm)
28" Commuter Bicycle Wheel (0.35 m) 0.35 0.35 m (350 mm) Standard 700c tire tread rolling radius
Utility Wind Turbine Blade (60 m) 60 60.0 meters Offshore 4 MW turbine blade tip rotation perimeter
Earth Equatorial Radius (6,378 km) 6378137 6,378,137 meters WGS 84 terrestrial equatorial geographic radius
Geostationary Orbital Radius (42,164 km) 4.2164 × 10⁷ 42,164,000 meters Satellite geosynchronous orbital perimeter radius
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Frequently Asked Questions

There are exactly 0.015707963 radians (rad) in 1 gradian (grad). To calculate larger amounts manually, simply multiply your total number of gradians by the conversion multiplier of 0.015707963.

The mathematical formula to convert gradians to radians is: [value] * 0.015707963 = radians. Rather than doing the math manually, you can use our high-precision online calculator to process this exact equation instantly without rounding errors.

To perform the reverse calculation from radians back to gradians, you must divide your starting value by 0.015707963. Our bidirectional tool automatically computes this inverse equation the moment you type into the radian input field.

1 Radian is larger than 1 Gradian. Specifically, 1 Gradian equals 0.015707963 radians, meaning 1 Radian is 63.662 times larger than 1 Gradian (a difference of 1.80 orders of magnitude). Expressing measurements in gradians requires a larger numerical value to represent the equivalent physical magnitude.

Under standard international measurement guidelines, 1 Gradian converts to 0.015707963 radians. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.

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