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Change Calculator from Radians to Degrees

Updated · Standard formula, shown below

The calculator for this page is switched off while it is checked. The formula is below, and the worked example in the article shows how to use it by hand.

Change Calculator from Radians to Degrees

To change a calculator from radians to degrees, look for a MODE button (often labeled DRG for Degrees, Radians, Gradians) and press it until the display shows DEG or D. On most scientific and graphing calculators, this cycles through the angle modes; on phone or computer calculator apps, the setting is usually in the app’s menu or a dedicated RAD/DEG toggle.

Formula

The conversion between radians and degrees is based on the fact that a full circle is 360 degrees and also 2Ï€ radians. Therefore:

  • Radians to degrees: multiply by 180 / Ï€
  • Degrees to radians: multiply by Ï€ / 180

In symbols: degrees = radians × (180 / π) and radians = degrees × (π / 180).

Worked Example

Using the default values above: you have an angle of 45° and the calculator is currently in Radians mode. To convert 45° to radians, use the formula:

radians = 45 × (π / 180) = 0.7854 (rounded to 4 decimal places).

If you instead wanted to convert 1 radian to degrees, you would compute 1 × (180 / π) = 57.2958°.

Why Does the Mode Matter?

Trigonometric functions like sine, cosine, and tangent expect the input angle in a specific unit. If you enter an angle in degrees while the calculator is in radian mode, the result will be wrong—often wildly so. For example, sin(30) in degree mode gives 0.5, but in radian mode it gives -0.988 (because 30 radians is about 1719 degrees). This is why checking the mode before any trig calculation is essential.

How to Change the Mode on Different Calculators

  • Texas Instruments (TI-30, TI-84): Press the MODE key, then use the arrow keys to highlight DEGREE and press ENTER. On the TI-84, you can also press 2nd then MODE (QUIT) after selecting.
  • Casio (fx-991EX, fx-260): Press SHIFT then SETUP (or MODE), then choose Deg (usually option 1) or Rad (option 2).
  • HP calculators: Often use a DEG or RAD label on the keyboard. Press the corresponding key or use the MODE menu.
  • Smartphone calculator apps: Rotate to landscape mode on iOS to see the scientific functions; the mode toggle is usually a small DEG/RAD button. Android apps vary—look for a settings gear or a RAD label.
  • Google Calculator: When you type a trig function, it assumes degrees by default, but you can add sin(30 rad) to force radians.

Common Mistakes and Misconceptions

One frequent error is forgetting that the mode also affects inverse trig functions (like sinâ�»Â¹). If you want an answer in degrees, the calculator must be in degree mode before you press the inverse key. Another misconception is that the mode changes the display of numbers—it doesn’t; it only affects how angles are interpreted in trig functions. Also, some calculators have a separate DMS (degrees, minutes, seconds) mode—that is not the same as degree mode for angles.

When to Use Radians vs. Degrees

Degrees are common in everyday geometry, navigation, and construction. Radians are the natural unit in calculus, physics, and most higher mathematics because formulas like the derivative of sine are simpler in radians. If you are solving a problem that involves π, radians are likely the intended unit. If the problem states angles in degrees, switch to degree mode.

Alternatives to Changing the Mode

If you cannot change the mode, you can convert manually using the formulas above. For example, to compute sin(30°) while in radian mode, enter sin(30 * π / 180). Many programming languages (Python, JavaScript) also default to radians; you can convert by multiplying by Math.PI / 180.

Frequently Asked Questions

How do I know if my calculator is in degrees or radians?

Look at the display. Most calculators show a small indicator like DEG, RAD, or GRAD in the corner. If you don’t see it, press the MODE button and the current mode will be highlighted.

What if my calculator doesn’t have a MODE button?

Some basic calculators have a DRG key that cycles through modes. Others, especially simple four-function calculators, do not have trigonometric functions at all, so the mode is irrelevant. For online calculators, look for a dropdown labeled “Angle unit� or a toggle.

Does the mode affect the result of logarithms or exponents?

No. The angle mode only affects trigonometric functions and their inverses. Logarithms, exponents, and other functions are unaffected.

Why does my calculator give a different answer than my friend’s for the same problem?

Most likely one calculator is in degree mode and the other in radian mode. Check both displays. Also, some calculators use different conventions for inverse trig (e.g., returning results in degrees vs. radians) based on the mode.

Can I change the mode while a calculation is in progress?

Yes, but it will affect any subsequent trig functions. If you have already entered an expression, changing the mode might not retroactively change the result of a previously evaluated trig function. It’s best to set the mode before starting.

What is the difference between degrees and gradians?

Gradians (or grads) divide a full circle into 400 units. They are rarely used in everyday math but appear in some surveying and European engineering contexts. The MODE button cycles through DEG, RAD, and GRAD.

Related

Formula used
in angle | Angle value | ° | 45 | 0
sel mode | Current mode | Radians=1, Degrees=0
out converted | Converted value | ° | angle * (mode = 1 ? 180 / pi : 1) | 4

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.