Degrees to Radians Converter (+ Radians to Degrees & Gradians)🌎
Instantly convert degrees to radians, radians to degrees, and gradians. Includes a full reference table of common angles (30°, 45°, 60°, 90°, 180°, 360°) and exact conversion formulas used in math, physics, and programming.
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Need to convert degrees to radians — or the other way around? This calculator handles all three angle units: degrees (°), radians (rad), and gradians (grad). Radians are the standard in calculus, physics, and programming (Python, JavaScript, C++ all use radians for trig functions). Gradians are used in surveying and some European engineering fields. Enter any value, pick your units, and get the result instantly with a precision of 6 decimal places.
When to use this calculator
Trigonometry and calculus — most formulas and derivatives require radians
Programming (Python math.sin, JavaScript Math.sin, C++ std::sin all need radians)
Physics and engineering calculations with angular velocity, oscillations, wave functions
Surveying and geospatial work where gradians (grads) are the convention
Checking mental math when dealing with angles in any STEM field
Trigonometric Values at Common Angles (Degrees · Radians)
Exact sine, cosine, and tangent values for the standard reference angles — the lookup table that accompanies degree↔radian conversion in trigonometry.
Degrees
Radians
sin
cos
tan
0°
0
0
1
0
30°
π/6 ≈ 0.5236
1/2 = 0.5000
√3/2 ≈ 0.8660
√3/3 ≈ 0.5774
45°
π/4 ≈ 0.7854
√2/2 ≈ 0.7071
√2/2 ≈ 0.7071
1
60°
π/3 ≈ 1.0472
√3/2 ≈ 0.8660
1/2 = 0.5000
√3 ≈ 1.7321
90°
π/2 ≈ 1.5708
1
0
undefined
120°
2π/3 ≈ 2.0944
√3/2 ≈ 0.8660
−1/2 = −0.5000
−√3 ≈ −1.7321
135°
3π/4 ≈ 2.3562
√2/2 ≈ 0.7071
−√2/2 ≈ −0.7071
−1
150°
5π/6 ≈ 2.6180
1/2 = 0.5000
−√3/2 ≈ −0.8660
−√3/3 ≈ −0.5774
180°
π ≈ 3.1416
0
−1
0
Radians = degrees × π/180. tan is undefined at 90° because cos 90° = 0 (division by zero). Decimal values rounded to 4 places. These are the exact 'unit-circle' values memorized in trigonometry.
How it works
How to Convert Degrees to Radians
The degree-to-radian conversion uses the simple formula:
> radians = degrees × π/180
Because a full circle spans both 360° and 2π radians, the conversion factor is π/180 ≈ 0.017453.
To reverse (radians → degrees), multiply by 180/π ≈ 57.2958.
Degrees to Radians: Reference Table
Degrees
Exact Radians
Decimal Radians
Gradians
0°
0
0.000000
0 grad
30°
π/6
0.523599
33.333 grad
45°
π/4
0.785398
50 grad
60°
π/3
1.047198
66.667 grad
90°
π/2
1.570796
100 grad
120°
2π/3
2.094395
133.333 grad
135°
3π/4
2.356194
150 grad
150°
5π/6
2.617994
166.667 grad
180°
π
3.141593
200 grad
270°
3π/2
4.712389
300 grad
360°
2π
6.283185
400 grad
Radians to Degrees Table
Radians
Decimal
Degrees
π/6
0.5236
30°
π/4
0.7854
45°
π/3
1.0472
60°
π/2
1.5708
90°
π
3.1416
180°
2π
6.2832
360°
All Conversion Formulas
Degrees → Radians: rad = deg × π/180
Radians → Degrees: deg = rad × 180/π
Degrees → Gradians: grad = deg × 10/9
Gradians → Degrees: deg = grad × 9/10
Radians → Gradians: grad = rad × 200/π
Gradians → Radians: rad = grad × π/200
Three Angle Units Compared
Unit
Full circle
Right angle
Use case
Degrees (°)
360
90°
Everyday geometry, maps, navigation
Radians (rad)
2π ≈ 6.283
π/2 ≈ 1.571
Calculus, physics, programming
Gradians (grad)
400
100
Surveying, European engineering
Why Radians Are Used in Calculus and Programming
Radians are the natural unit because the arc length of a unit circle equals the angle in radians. This makes calculus formulas simpler: d/dx[sin(x)] = cos(x) only when x is in radians. In degrees, you'd need a correction factor of π/180. That's why Python's math.sin(), JavaScript's Math.sin(), and virtually every scientific library expect radians by default.
Multiply the degree value by π/180 (≈ 0.017453). Example: 90° × π/180 = π/2 ≈ 1.5708 radians. For the reverse, multiply radians by 180/π (≈ 57.2958).
What is π/2 in degrees?
π/2 radians = 90 degrees. This is a right angle. Other key values: π/4 = 45°, π/3 = 60°, π = 180°, 2π = 360°.
Why does Python (and JavaScript) use radians, not degrees?
All programming trig functions (math.sin, Math.cos, etc.) take radians because the arc length on a unit circle equals the angle in radians — making formulas simpler and derivatives work without correction factors. Always convert your degrees first: radians = degrees * math.pi / 180.
What are gradians and who uses them?
Gradians (grads) divide a right angle into 100 units, so a full circle = 400 grad. They are used in surveying and some European engineering and military fields. Scientific calculators often label the grad mode as 'G' or 'GRAD'.
How many radians is 1 degree?
1° = π/180 ≈ 0.017453 radians. Conversely, 1 radian ≈ 57.2958°. A radian is roughly 57.3 degrees — the angle whose arc on a unit circle has length 1.
How do I convert 45 degrees to radians?
45° × π/180 = π/4 ≈ 0.785398 radians. This is one of the most common conversions in trigonometry, corresponding to the 45-45-90 triangle and sin(45°) = cos(45°) = √2/2.
What is 1 radian in degrees?
1 radian = 180/π ≈ 57.2958 degrees. This follows directly from the definition: a radian is the angle subtended at the center of a circle by an arc equal in length to the radius.
How do I convert radians to gradians?
Multiply by 200/π ≈ 63.6620. Example: π/2 rad × 200/π = 100 grad (a right angle). To go from gradians to radians, multiply by π/200.
What is 180 degrees in radians?
180° = π radians ≈ 3.141593 rad. This is a straight angle (half rotation). It's one of the most important values in trigonometry and the definition of π itself in the context of circle geometry.
What is 360 degrees in radians?
360° = 2π radians ≈ 6.283185 rad. This is one full rotation. It also equals 400 gradians. The value 2π appears constantly in physics (angular frequency, wave equations) and geometry.
Calculadora de matemática revisada por el equipo editorial de Hacé Cuentas, contrastada con Wolfram MathWorld — Radian definition and conversions, según nuestra política editorial y metodología.
Updates
Última revisión: June 22, 2026. Los parámetros se verifican periódicamente con las fuentes citadas.
Privacy
Calculations run 100% in your browser. We do not store or transmit your data.
Limitations
Indicative results. For critical decisions, consult a professional.
📌 How to cite this calculator
Rodríguez, M. (2026). Degrees to Radians Converter (+ Radians to Degrees & Gradians). Hacé Cuentas. https://hacecuentas.com/conversion-degrees-radians-gradians
Contenido bajo licencia CC-BY 4.0 — reutilizable citando la fuente con enlace a Hacé Cuentas.
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