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Degrees to Radians Converter

Convert angles between degrees and radians with optional gradians and turns for engineering and math work.

Formula shown0 inputs definedUpdated Nov 2025By CalcuTotal TeamFree, no sign-up

Quick Summary

Use this when you need:

Prepare inputs for trig functions that expect radians
Translate CAD dimensions expressed in degrees into radians for scripts
Compare navigation bearings in degrees against math libraries that use turns or gradians

You’ll get:Angle

How this is calculated

Formula:

radians = degrees * pi / 180

In plain language:

The calculator normalizes to degrees and applies the exact factor pi/180 to reach radians, while also offering gradians (deg*10/9) and turns (deg/360).

The formula is always visible so you can verify the math and explain your numbers to anyone who asks.

What these terms mean

Angle

Angle used in the calculation.

When to use this calculator

Prepare inputs for trig functions that expect radians
Translate CAD dimensions expressed in degrees into radians for scripts
Compare navigation bearings in degrees against math libraries that use turns or gradians

Last updated: November 25, 2025

Degrees to radians converter explained

Most programming languages and calculators expect angles in radians, while humans think in degrees. This converter bridges the two, with gradians and turns available if you work in surveying or rotation-heavy contexts.

How the conversion works

Radians relate to degrees by $\pi$ : $\text{rad} = \text{deg} \times \pi / 180$ .
$1\ \text{rad} \approx 57.2957795131^\circ$ .
$1\ \text{turn} = 360^\circ = 2\pi\ \text{rad}$ .
$1\ \text{gradian} = 0.9^\circ$ .

The calculator normalizes to degrees, applies the appropriate factor, and presents the target unit with clear rounding.

Quick examples

$180^\circ \rightarrow 180 \times \pi / 180 = \pi\ \text{rad} \approx 3.14159$
$1\ \text{rad} \rightarrow 1 \times 57.2957795131 \approx 57.29578^\circ$
$90^\circ \rightarrow 90 / 360 = 0.25\ \text{turns}$

Tips

Feed radians into trig functions (sin, cos, etc.) to avoid silent unit bugs.
Keep more decimals when converting small angles; rounding too early skews results in physics or graphics code.
Gradians (400 grads in a full turn) show up in some surveying gear—toggle them if you need compatibility.

Units and conversions

Unit	Symbol	Relation
Degree	°	base
Radian	rad	$1\ \text{rad} = 57.2957795131^\circ$
Gradian	gon	$1\ \text{gon} = 0.9^\circ$
Turn	turn	$1\ \text{turn} = 360^\circ = 2\pi\ \text{rad}$

Worked examples

CAD angle to radians
Sketch calls for $35^\circ$ .
$\text{rad} = 35 \times \pi / 180 \approx 0.6109$
Result: ≈0.6109 rad.
Robotics joint output
Controller reports $1.4\ \text{rad}$ .
$\text{deg} = 1.4 \times 57.2957795131 \approx 80.324$
Result: ≈80.32°.
Survey gear in grads
Bearing: $120\ \text{gon}$ .
$\text{deg} = 120 \times 0.9 = 108^\circ \\ \text{rad} = 108 \times \pi / 180 \approx 1.88496$
Result: ≈1.885 rad.

References and further reading

Frequently Asked Questions

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Calculator info

Version:: v1.0.0
Last reviewed:: Nov 25, 2025
Sensitivity:: low

Last updated: November 25, 2025

Degrees to radians converter explained

How the conversion works

Radians relate to degrees by $\pi$ : $\text{rad} = \text{deg} \times \pi / 180$ .
$1\ \text{rad} \approx 57.2957795131^\circ$ .
$1\ \text{turn} = 360^\circ = 2\pi\ \text{rad}$ .
$1\ \text{gradian} = 0.9^\circ$ .

The calculator normalizes to degrees, applies the appropriate factor, and presents the target unit with clear rounding.

Quick examples

$180^\circ \rightarrow 180 \times \pi / 180 = \pi\ \text{rad} \approx 3.14159$
$1\ \text{rad} \rightarrow 1 \times 57.2957795131 \approx 57.29578^\circ$
$90^\circ \rightarrow 90 / 360 = 0.25\ \text{turns}$

Tips

Feed radians into trig functions (sin, cos, etc.) to avoid silent unit bugs.
Keep more decimals when converting small angles; rounding too early skews results in physics or graphics code.
Gradians (400 grads in a full turn) show up in some surveying gear—toggle them if you need compatibility.

Units and conversions

Unit	Symbol	Relation
Degree	°	base
Radian	rad	$1\ \text{rad} = 57.2957795131^\circ$
Gradian	gon	$1\ \text{gon} = 0.9^\circ$
Turn	turn	$1\ \text{turn} = 360^\circ = 2\pi\ \text{rad}$

Worked examples

CAD angle to radians
Sketch calls for $35^\circ$ .
$\text{rad} = 35 \times \pi / 180 \approx 0.6109$
Result: ≈0.6109 rad.
Robotics joint output
Controller reports $1.4\ \text{rad}$ .
$\text{deg} = 1.4 \times 57.2957795131 \approx 80.324$
Result: ≈80.32°.
Survey gear in grads
Bearing: $120\ \text{gon}$ .
$\text{deg} = 120 \times 0.9 = 108^\circ \\ \text{rad} = 108 \times \pi / 180 \approx 1.88496$
Result: ≈1.885 rad.

Quick Summary

Calculator Tool

How this is calculated

What these terms mean

Angle

When to use this calculator

Degrees to radians converter explained

How the conversion works

Quick examples

Tips

Units and conversions

Worked examples

References and further reading

Frequently Asked Questions

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Calculator info

Degrees to radians converter explained

How the conversion works

Quick examples

Tips

Units and conversions

Worked examples

References and further reading

Frequently Asked Questions

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