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Radian to Grad (rad to grad) Calculator & Formula

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Live Conversion • ISO 80000-3:2019 Certified
1 Radian = 63.66197724 Grad
1 rad = 63.661977 grad • 1 grad = 0.015708 rad
Radian to Grad: One Radian is equal to 63.66197724 Grads.
Certified Authority Value
63.66197724
grad
Exact: 1 grad ≡ 0.01570796327 rad
rad
rad
Swap to Grad to Radian
grad
grad 63.66197724
Quick Values:
1 rad 5 rad 10 rad 25 rad 50 rad 100 rad 250 rad 500 rad 1,000 rad
Conversion Formula
To convert Radian to Grad, multiply by 63.66197724
rad × 63.66197724 = grad

Calculation: 1 rad × 63.66197724 = 63.66197724 grad

Common Radian to Grad Calculations

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

Tap any row to calculate
Grad to Radian: Reciprocal Summary
Grad to Radian Conversion Reference Table
Reciprocal & Equivalent Value Scientific Notation
1 grad is equal to 0.015708 rad (Radian) 1.571 × 10⁻²
5 grad is equal to 0.0785398 rad (Radian) 7.854 × 10⁻²
10 grad is equal to 0.15708 rad (Radian) 1.571 × 10⁻¹
50 grad is equal to 0.785398 rad (Radian) 7.854 × 10⁻¹
100 grad is equal to 1.570796 rad (Radian) 1.571 × 10⁰
View Complete 15-Row Grad to Radian 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 Radian (rad) and Grad (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

Grad References:

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

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

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

How to Convert Radian to Grad

Converting Radian (rad) to Grad (Grad) is a core calculation in Plane Angle, which measures the circular arc subtended between two intersecting rays or diverging lines. Because Radian represents a larger magnitude than Grad, converting from rad to Grad expands the numerical figure. Exactly 1 Radian encompasses 63.661977 Grad. To convert any quantity, multiply the value in Radian by 63.661977.

Direct Factor1 rad = 63.661977 Grad
Inverse Ratio1 Grad = 0.015708 rad
Conversion ScaleDirect Proportional Magnitude Expansion
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 rad = 57.29578 radian (rad)
2. Target SI Bridge (ktarget):1 Grad = 0.9 radian (rad)
Step-by-step substitution for Radian → Grad:V(Grad) = V(rad) × ( 57.29578 / 0.9 ) = V(rad) × 63.661977
Mathematical FormulaValue in Grad = Value in Radian × 63.66197724Direct computational formula applied for standard conversion.
Worked Example

Converting 250 rad yields an exact output of 15915.494309 Grad in Grad. Under higher industrial throughput, 1000 rad translates to 63661.977237 Grad.

Inverse check: 1 Grad = 0.015708 rad.

Understanding Radian and Grad

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

Grad

Grad
Standard Unit

A 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

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 Grad
Subtended angle of arc equal in length to circle radius (~57.3°)1 rad63.661977 Grad
Complete circular rotation angle expressed in radians (2π rad / 6.283 rad)6.283 rad399.988203 Grad
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].

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Frequently Asked Questions

There are exactly 63.66197724 grads (grad) in 1 radian (rad). To calculate larger amounts manually, simply multiply your total number of radians by the conversion multiplier of 63.66197724.

The mathematical formula to convert radians to grads is: [value] * 63.66197724 = grads. 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 grads back to radians, you must divide your starting value by 63.66197724. Our bidirectional tool automatically computes this inverse equation the moment you type into the grad input field.

1 Radian is larger than 1 Grad. Specifically, 1 Radian equals exactly 63.66197724 grads, making it 63.662 times larger (a difference of 1.80 orders of magnitude). Therefore, quantities expressed in grads require a larger numerical value to represent the same physical amount.

A typical subtended angle of arc equal in length to circle radius (~57.3°) measures 1 rad, which corresponds to 63.662 Grad (Grad).

Exactly 1 rad = 200/π ≈ 63.6619772368 grad (rounded to 63.662 grad). A full circle is 2π radians = 400 grad, so 1 rad = 400 / (2π) = 200/π.

Multiply the radian value by 200/π (or 63.6619772368). KaTeX: V(grad) = V(rad) × 200 / π ≈ V(rad) × 63.662. Example: π/2 rad × 63.662 = 100 grad (right angle).

Multiply the grad value by π/200 (or 0.01570796327). KaTeX: V(rad) = V(grad) × π / 200 ≈ V(grad) × 0.015708. Example: 200 grad × 0.015708 = 3.14159 rad = π.

Grads (gons) are standard in surveying, civil engineering, and European cartography. A right angle is exactly 100 grad, simplifying decimal subdivision. Theodolites and total stations often display in grads; 1 grad = 0.9 ° = 54 '.

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