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Radian to degree - How to convert rad to °
In mathematics, engineering, and navigation, radians and degrees are two different ways to measure the same thing — the size of an angle. Radians work naturally in formulas, while degrees are the measurement most people can picture instantly. Switching between them is a skill that appears in everything from classroom problems to spacecraft navigation.
Radian and Degree in Everyday and Technical Use
A radian (rad) is defined by the circle itself — it’s the angle created when the arc length equals the radius. A full rotation has 2π radians, which works out to about 6.28318 radians. Because of their direct link to a circle’s properties, radians are the go-to choice in trigonometry, calculus, and physics.
A degree (°) breaks a circle into 360 equal parts, a method inherited from ancient Babylonian astronomers who used a base-60 counting system. Degrees are familiar, practical, and easier for most people to visualize, which is why they’re common in navigation, mapping, and engineering plans.
Converting Radians to Degrees
The formula is simple and consistent:
Degrees (°) = Radians (rad) × 180 ÷ π
Examples:π rad × 180 ÷ π = 180°π⁄2 rad × 180 ÷ π = 90°
If you want an instant result, the Angle Conversion calculator on Jetcalculator will do the math in seconds.
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Do you know?
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One radian equals about 57.2958°, and this number never changes.
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Radians make certain equations in calculus shorter and easier to work with.
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Many computer programming functions take input in radians, not degrees.
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The concept of radians existed long before it became an official unit in the 19th century.
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Some scientific calculators default to radians, which can cause mistakes if you expect degree results.
The Apollo 13 Re-Entry Calculations
In April 1970, Apollo 13 suffered a catastrophic explosion en route to the Moon, forcing the crew to abort their mission. To return to Earth, they needed to re-enter the atmosphere at a precise angle. If they came in too steep, they risked burning up; too shallow, and they’d skip back into space.
Mission control engineers performed the math in radians, which simplified the trigonometric calculations needed for the spacecraft’s trajectory. But the astronauts had to see and align to a degree of measurement through the limited visibility of the spacecraft’s small windows. Every adjustment was converted using Degrees = Radians × 180 ÷ π.
Even a half-degree error could have spelled disaster. The success of this manual conversion process — under intense pressure and with lives at stake — helped bring all three astronauts home safely. It remains one of history’s best examples of how a small calculation can change everything.
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Wrapping it up
Converting radian to degree (rad to °) might look like a quick multiplication, but it’s a bridge between the abstract world of mathematics and the practical reality of navigation, design, and science. The simple relationship Degrees = Radians × 180 ÷ π quietly powers countless tasks, from plotting an engineering project to aiming a telescope at a distant star.
For more than just angles, the Conversion Tools section on Jetcalculator has fast, reliable calculators for distances, temperatures, and more — making sure your results are always spot on.
