How to Use This Angle Converter
We designed this tool to be as easy as possible. Here’s how it works:
- Select Your ‘From’ Unit: In the “From” box, choose the unit you have. For example,
degree (°). - Select Your ‘To’ Unit: In the “To” box, choose the unit you want. For example,
radian (rad). - Enter Your Value: Type the number you want to convert into the “Value to Convert” field.
- Click “Calculate”: And… that’s it! Your new, converted angle will appear instantly in the “Answer” box.
Need to start over? Just hit the “Clear” button for a fresh calculation.
Why You’ll Love This Tool
- It’s Instant: No loading times, no waiting. You get your answer right away.
- It’s Accurate: We use the standard mathematical formulas to ensure your conversions are always precise.
- It’s Easy to Use: The interface is clean and straightforward. You don’t need to be a math whiz to use it.
- It’s Comprehensive: We cover all the common (and even some uncommon) units, including degrees, radians, and gradians.
Understanding the Angles (A Quick Refresher)
Not sure what the difference is between all these units? Here’s a simple breakdown. Think of an angle as just a way to measure the “amount of turn” between two lines.
What is a Degree (°)?
This is the one you’re probably most familiar with. A full circle is divided into 360 degrees.
- A right angle (like the corner of a square) is 90°.
- A straight line is 180°.
- A full circle or one complete revolution is 360°.
What is a Radian (rad)?
Radians are the standard unit for angles in mathematics, physics, and programming. It all relates to the radius of a circle and the number Pi ($\pi$).
- A straight line (180°) is equal to $\pi$ radians (about 3.14159).
- A full circle (360°) is equal to $2\pi$ radians (about 6.283).
It might seem complex, but it makes many math equations much simpler, which is why it’s used so often.
What is a Gradian (grad)?
This one is less common but very logical. The gradian (also called “gon”) divides a circle into 400 parts.
- A right angle is 100 grad.
- A full circle is 400 grad.It’s a “metric” version of an angle, which can be easier for some calculations.
Let’s See it in Action: A Quick Example
Want to know how many radians are in a standard 45° angle?
- Set From:
degree (°) - Set To:
radian (rad) - Enter Value: 45
- Click Calculate
Answer: You’ll get 0.78539… (which is the same as $\pi/4$). Easy!
Frequently Asked Questions (FAQs)
Q1: What is the most common angle conversion?
A: By far, the most common conversion is between degrees and radians. This is because degrees are used in everyday life, while radians are the standard for trigonometry, calculus, and physics.
Q2: Why is a circle 360 degrees?
A: This actually dates back to the ancient Babylonians! They used a base-60 (sexagesimal) number system. The number 360 is very convenient because it can be divided evenly by many numbers (2, 3, 4, 5, 6, 8, 9, 10, 12, and more), which made it easy for them to divide a circle into equal parts.
Q3: How do you convert degrees to radians manually?
A: If you ever want to do it yourself, the formula is simple:
$\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$
And to go the other way:
$\text{Degrees} = \text{Radians} \times \frac{180}{\pi}$
…or you could just use this tool and save yourself the trouble!