A degree is a versatile unit used to measure angles, temperature, and even geographic coordinates. When it comes to angles, the degree’s origin traces back to ancient Babylon, where mathematicians used a base-60 number system. This influence is why there are 360 degrees in a circle—a number easily divisible into many integer parts, allowing for precise calculations.

In navigation and cartography, degrees are crucial for pinpointing locations on Earth’s surface through latitude and longitude. Notably, each degree of latitude encompasses about 111 kilometers on the planet’s surface. Meanwhile, in temperature measurement, degrees Fahrenheit and Celsius reveal a fascinating convergence: −40°F is equivalent to −40°C, a curiosity often unknown by many. These uses highlight the degree’s essential role across various fields of science and everyday life.

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A radian is a unit of angular measure used in mathematics and is crucial for its ability to maintain consistency in trigonometric calculations. It is defined as the angle formed when the arc length equals the radius of the circle. Unlike degrees, radians offer a natural connection to the properties of a circle, as there are \(2\pi\) radians in a full circle, reflecting the direct relationship with the circle’s circumference. Interestingly, radians are dimensionless, meaning they have no physical dimension, which makes them an extremely versatile unit across different applications in physics and engineering.

Radian’s significance extends beyond just academic circles; it forms the backbone of much of modern technology. For example, the calculations performed by digital devices like smartphones and computers in graphic rendering and signal processing rely heavily on radian-based trigonometry. This seamless integration into practical technology underscores the profound yet often unnoticed role radians play in our digital world. By using radians, we achieve more efficient and accurate results, highlighting their indispensable nature in both theoretical and applied sciences.

Degrees

Radians

0 deg

0 rad

5 deg

0.0872665 rad

10 deg

0.174533 rad

15 deg

0.261799 rad

20 deg

0.349066 rad

25 deg

0.436332 rad

30 deg

0.523599 rad

35 deg

0.610865 rad

40 deg

0.698132 rad

45 deg

0.785398 rad

50 deg

0.872665 rad

55 deg

0.959931 rad

60 deg

1.0472 rad

65 deg

1.13446 rad

70 deg

1.22173 rad

75 deg

1.309 rad

80 deg

1.39626 rad

85 deg

1.48353 rad

90 deg

1.5708 rad

95 deg

1.65806 rad

100 deg

1.74533 rad

105 deg

1.8326 rad

110 deg

1.91986 rad

115 deg

2.00713 rad

120 deg

2.0944 rad

125 deg

2.18166 rad

130 deg

2.26893 rad

135 deg

2.35619 rad

140 deg

2.44346 rad

145 deg

2.53073 rad

150 deg

2.61799 rad

155 deg

2.70526 rad

160 deg

2.79253 rad

165 deg

2.87979 rad

170 deg

2.96706 rad

175 deg

3.05433 rad

180 deg

3.14159 rad

185 deg

3.22886 rad

190 deg

3.31613 rad

195 deg

3.40339 rad

200 deg

3.49066 rad

205 deg

3.57792 rad

210 deg

3.66519 rad

215 deg

3.75246 rad

220 deg

3.83972 rad

225 deg

3.92699 rad

230 deg

4.01426 rad

235 deg

4.10152 rad

240 deg

4.18879 rad

245 deg

4.27606 rad

250 deg

4.36332 rad

255 deg

4.45059 rad

260 deg

4.53786 rad

265 deg

4.62512 rad

270 deg

4.71239 rad

275 deg

4.79966 rad

280 deg

4.88692 rad

285 deg

4.97419 rad

290 deg

5.06145 rad

295 deg

5.14872 rad

300 deg

5.23599 rad

305 deg

5.32325 rad

310 deg

5.41052 rad

315 deg

5.49779 rad

320 deg

5.58505 rad

325 deg

5.67232 rad

330 deg

5.75959 rad

335 deg

5.84685 rad

340 deg

5.93412 rad

345 deg

6.02139 rad

350 deg

6.10865 rad

355 deg

6.19592 rad

360 deg

6.28319 rad

Conversion

Degrees to Gradians

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Degrees to Arcminutes

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Degrees to Arcseconds

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Degrees to Radians Conversion

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> Degrees to Radians Conversion Table

> Other Conversions

:: Angle Units

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> Degrees to Radians Conversion Table

> Other Conversions

:: Angle Units

:: Spread the Word

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