Trigonometry Radians to Degrees Calculator

Convert radians to degrees with steps and charts. Check quadrants, reference angles, coterminals, and exports. Learn trigonometry angle conversion with clear results very quickly.

Result

1.570796 radians equals 90 degrees.

Formula applied: degrees = radians × 180 ÷ π.

Degrees 90°
Normalized Angle 90°
Reference Angle 90°
Quadrant or Axis On positive y-axis
Degrees Minutes Seconds 90° 0' 0"
Signed Normal Range 90°

Calculator Inputs

Use values like 1.5708, pi/2, or 3*pi/4.
This field is used in decimal mode.
Example: 0.5 means π/2 radians.
Choose 0 to 10 decimal places.
Separate values by line, comma, or semicolon.
Degrees and DMS
Reference angle
Quadrant check
Coterminal angles
Trig values

Detailed Trigonometry Results

Radians 1.570796
Degrees 90°
Normalized 0° to 360° 90°
Normalized -180° to 180° 90°
Reference Angle 90°
Quadrant or Axis On positive y-axis
Degrees Minutes Seconds 90° 0' 0"
Turns 0.25
Gradians 100 gon
Arcminutes 5400
Arcseconds 324000.000001
NATO Mils 1600
Positive Coterminal Angle 450°
Negative Coterminal Angle -270°
Sine 1
Cosine 0
Tangent Undefined

Angle Graph

The line shows the converted angle position on the unit circle.

Batch Conversion Table

Input Radians Degrees Normalized Angle Reference Angle Quadrant
0 0 On positive x-axis
pi/6 0.523599 30° 30° 30° Quadrant I
pi/4 0.785398 45° 45° 45° Quadrant I
pi/2 1.570796 90° 90° 90° On positive y-axis
pi 3.141593 180° 180° On negative x-axis
2*pi 6.283185 360° On positive x-axis

Formula Used

The calculator converts radians to degrees with the standard circle relation.

How to Use This Calculator

  1. Choose decimal mode for values like 1.5708 or expressions like pi/2.
  2. Choose coefficient mode when the angle is written as a multiple of π.
  3. Set the decimal precision for rounded results.
  4. Add batch angles if you want many conversions at once.
  5. Press calculate to view the result below the header.
  6. Use CSV for spreadsheet export.
  7. Use PDF for a printable result summary.

Example Data Table

Radians Degrees Reference Angle Common Use
0 Start of unit circle
π/6 30° 30° Special triangle angle
π/4 45° 45° Equal leg triangle
π/2 90° 90° Positive y-axis
π 180° Straight angle
360° Full rotation

Why radians and degrees matter

Angles appear in every part of trigonometry. Degrees feel familiar because a full circle has 360 degrees. Radians describe the same turn by using the circle radius. One radian is the angle made when the arc length equals the radius. This idea makes many formulas shorter. It also explains why radians are common in calculus, waves, physics, and advanced graph work.

Practical angle conversion

This calculator changes radians into degrees with clear steps. It accepts normal decimal radians. It also accepts values based on pi. That helps when your textbook gives angles like pi over six or three pi over four. The tool shows the main degree answer, normalized angles, coterminal angles, and the reference angle. It also reports the quadrant when the angle is not on an axis.

Better checking for assignments

A simple conversion can still create mistakes. Many students multiply by pi instead of dividing by it. Others forget that negative radians rotate clockwise. The detailed result helps catch those errors. The graph also gives a quick visual check. You can see the angle position on a unit circle and compare it with the quadrant result.

Advanced outputs

The calculator includes degrees, minutes, and seconds. It also shows turns, gradians, and arc seconds. These values are useful in surveying, navigation, engineering, optics, and technical drawing. Trigonometric values are included for fast review. Sine, cosine, and tangent are calculated from the original radian value, so the results remain consistent.

Exporting your work

Use the CSV option when you need spreadsheet records. Use the PDF option when you want a clean summary for notes, reports, or classroom review. The example table gives common radian values, so you can compare your answer with known results before submitting work.

When to normalize angles

Normalization is helpful when an answer passes one full rotation. An angle of 450 degrees points to the same final side as 90 degrees. The original value still matters, because it records total rotation. The normalized value helps with graphing, quadrant checks, and comparison. Choose the signed range when direction around zero is important. It keeps long angle reports easy to read later.

FAQs

1. What is the formula for radians to degrees?

Multiply the radian value by 180, then divide by pi. The formula is degrees = radians × 180 ÷ π.

2. Why do trigonometry problems use radians?

Radians connect angles directly with arc length and radius. This makes many formulas simpler in calculus, waves, circular motion, and graphing.

3. What is pi radians in degrees?

Pi radians equals 180 degrees. A full circle is 2π radians, which equals 360 degrees.

4. Can I enter values like pi over two?

Yes. Enter values like pi/2, pi/6, 3*pi/4, or 2*pi in decimal mode. The calculator parses common pi expressions.

5. What is a reference angle?

A reference angle is the acute angle between the terminal side of an angle and the x-axis. It helps compare trig values.

6. What does normalized angle mean?

A normalized angle is reduced to a standard range, such as 0 to 360 degrees. It shows the final position after full turns.

7. Why is tangent sometimes undefined?

Tangent equals sine divided by cosine. When cosine is zero, division is not possible, so tangent is undefined.

8. Can I export multiple conversions?

Yes. Add batch values in the text box. Then use the CSV export to save the full batch table.

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