Convert any angle between degrees and radians instantly, with exact π form shown for common angles.
Enter a degree or radian value and pick a convert button
| Degrees | Radians (exact) | Radians (decimal) |
|---|---|---|
| 0° | 0 | 0.000000 |
| 30° | π/6 | 0.523599 |
| 45° | π/4 | 0.785398 |
| 60° | π/3 | 1.047198 |
| 90° | π/2 | 1.570796 |
| 120° | 2π/3 | 2.094395 |
| 135° | 3π/4 | 2.356194 |
| 150° | 5π/6 | 2.617994 |
| 180° | π | 3.141593 |
| 270° | 3π/2 | 4.712389 |
| 360° | 2π | 6.283185 |
This degrees to radians calculator (and radians to degrees calculator) converts any angle between the two most common ways of measuring rotation, showing both a decimal result and — for common angles — the exact π-fraction form like π/4 or 3π/2. As a combined angle unit converter and pi radians calculator, it also includes a full reference table of standard angle pairs so you can look up a common conversion without doing the math yourself.
Degrees and radians are two different scales for measuring the same thing: rotation around a circle. Degrees split a full circle into 360 equal parts, a convention dating back to ancient Babylonian astronomy. Radians instead measure rotation by arc length: one radian is the angle where the arc length equals the circle's radius, making a full circle exactly 2π radians. This converter translates any value between the two, both as a decimal and — where possible — as a clean fraction of π.
This tool is built for trigonometry, precalculus, and calculus students who need to switch between degree-based problems and radian-based formulas, programmers converting user-facing degree inputs into the radians expected by math libraries, physics and engineering students working with angular velocity or angular acceleration, and anyone double-checking a π-fraction angle like π/6 or 5π/4.
Radians aren't just an alternative notation — they're the natural unit for calculus and physics. Derivatives and integrals of trigonometric functions only take their simplest form when the angle is in radians; in degrees, extra conversion constants creep into every formula. This is also why programming languages and math libraries (including JavaScript's Math.sin, Math.cos, and Math.tan) universally expect radian input, making degree-to-radian conversion a routine step in any angle-based code.
Programmers convert user-entered degree values into radians before calling trig functions in JavaScript, Python, or any C-family language. Physicists and mechanical engineers express angular velocity and angular acceleration natively in radians per second. Calculus students convert degree-based problems into radians before differentiating or integrating trig functions. Navigators and surveyors move between degree-based bearings and radian-based calculations. Computer graphics programmers typically need radians for rotation transformations.
How this calculator converts an angle in either direction, with exact π form
Degrees divide a circle into 360 parts; radians measure rotation by arc length, making a full circle exactly 2π radians.
Angles like 30°, 45°, 60°, and 90° reduce to clean fractions of π (π/6, π/4, π/3, π/2) — this calculator shows both forms.
JavaScript's Math.sin/cos/tan and virtually every programming math library expect angle arguments in radians, not degrees.
From entering an angle to reading the exact and decimal result
Use the Degrees field if you're converting to radians, or the Radians field if you're converting to degrees.
Type any degree or radian value, including negative angles or values beyond 360°/2π.
Click "Convert to Radians" or "Convert to Degrees" depending on which field you filled in.
See the decimal value and, for common angles, the exact π-fraction form shown side by side.
Scroll to the Common Angle Reference table for a quick lookup of standard degree/radian pairs without recalculating.
Convert your result back the other direction and confirm it returns your original angle.
Converting 45° to radians, then converting back to confirm
Convert 45° to radians, in both exact and decimal form, then verify the conversion by converting back to degrees.
Explanation: 45° reduces to π/4 because 45/180 simplifies to the fraction 1/4 — this calculator checks denominators up to 12 to find this kind of clean reduction automatically. Converting the result back through the reverse formula returning exactly 45° is a fast, reliable way to confirm any degree-radian conversion.
Reading the exact form, the decimal, and when no exact form exists
| Result Field | What It Means |
|---|---|
| Decimal | The radian or degree value as a standard floating-point number, always shown regardless of the angle |
| Exact (π form) | The angle written as a simplified fraction of π — shown only when the denominator (after simplifying) is 12 or less |
| "No simple π form" | The angle does not reduce to a clean fraction of π within a denominator of 12 — this is normal, not an error |
Reading the exact form: a result like "π/4 (0.785398)" means the angle is exactly one-eighth of a full 2π rotation — the decimal is simply that fraction's numeric value.
Reading "No simple π form": this appears for angles like 50° or 100° that don't reduce cleanly — the decimal value is still fully accurate, it just has no tidy fractional representation.
Manual verification: the fastest sanity check is converting your result back through the opposite formula — it should return your original input, since 180° = π radians is the fixed anchor point both directions share.
Where fast, reliable angle unit conversion is genuinely useful
Check degree-to-radian and radian-to-degree homework conversions instantly.
Quickly verify π-fraction conversions used throughout precalculus and calculus tests.
Convert user-facing degree inputs into radians before calling Math.sin, Math.cos, or Math.tan.
Convert between degree and radian measurements for angular velocity and acceleration formulas.
Convert degree-based angle problems into radians before differentiating or integrating trig functions.
Move between degree-based bearings and radian-based calculation systems.
Convert degree-based rotation inputs into the radians most rendering engines expect.
Convert joint or motor rotation specs between degree and radian conventions.
Convert angular measurements between degrees and radians for orbital and positional calculations.
Translate angle specifications between the two unit systems used across different software tools.
Cross-check the unit selector on other calculators by confirming your angle's radian equivalent first.
Convert phase angles between degrees and radians when working across different libraries or datasets.
What this angle unit converter does well, and where it has limits
The standard angle pairs used constantly in trigonometry and calculus
| Degrees | Radians (exact) | Radians (decimal) |
|---|---|---|
| 0° | 0 | 0.000000 |
| 30° | π/6 | 0.523599 |
| 45° | π/4 | 0.785398 |
| 60° | π/3 | 1.047198 |
| 90° | π/2 | 1.570796 |
| 180° | π | 3.141593 |
| 270° | 3π/2 | 4.712389 |
| 360° | 2π | 6.283185 |
Summary: This degrees ↔ radians converter gives you an instant, free way to convert any angle in either direction, with exact π-fraction form shown for common angles. Pair it with related tools like the Trig Function Calculator and Unit Circle Calculator for a fuller picture of angle-based trigonometry.
Common questions about degree and radian conversion
Trusted educational references to go deeper on radian and degree conversion
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