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Degree Symbol — Definition, Formula & Examples

The degree symbol (°) is the small raised circle written right after a number to show that the number measures an angle in degrees or a temperature in degrees. For example, 90° means "90 degrees" and 72°F means "72 degrees Fahrenheit."

The degree symbol, denoted °, is a typographic mark placed immediately after a numeral (with no space) to indicate that the quantity is expressed in the unit called a degree. In mathematics it most commonly signifies an angle measured in the degree-of-arc system, where a full rotation equals 360°. In science and everyday life it also appears in temperature scales (°C, °F, K is an exception — kelvins omit the symbol).

Key Formula

n° means n degreesn°\text{ means }n\text{ degrees}
Where:
  • nn = A number representing the size of an angle or a temperature reading
  • °° = The degree symbol, indicating the unit is degrees

How It Works

You write the degree symbol as a small superscript circle touching the upper-right side of the number: 45°45°, not 45°45 ° or 45°45^\circ{}°. In math class, the symbol tells you the angle is measured in degrees rather than in radians or some other unit. When you see A=60°\angle A = 60°, read it aloud as "angle A equals 60 degrees." On a keyboard you can type the symbol by pressing Alt + 0176 on Windows, Option + Shift + 8 on Mac, or by inserting a special character. In handwriting, simply draw a tiny circle at the top-right of the number. In typed math (LaTeX or KaTeX), the command ^\circ produces the degree symbol: 4545^\circ.

Worked Example

Problem: A triangle has angles of 50° and 60°. Use the degree symbol correctly to find and write the third angle.
Step 1: Recall that the three angles of any triangle add up to 180°.
A+B+C=180°\angle A + \angle B + \angle C = 180°
Step 2: Substitute the two known angles.
50°+60°+C=180°50° + 60° + \angle C = 180°
Step 3: Add the known angles.
110°+C=180°110° + \angle C = 180°
Step 4: Subtract to find the missing angle. Write the degree symbol right after the number with no space.
C=180°110°=70°\angle C = 180° - 110° = 70°
Answer: The third angle is 70°.

Another Example

This example shows the degree symbol used for temperature instead of angles, reinforcing that the same symbol appears in both contexts.

Problem: The temperature outside is 32°F. Convert this to Celsius and write the answer with the correct degree symbol notation.
Step 1: Use the Fahrenheit-to-Celsius formula.
C=59(F32)C = \frac{5}{9}(F - 32)
Step 2: Substitute 32 for F.
C=59(3232)=59(0)C = \frac{5}{9}(32 - 32) = \frac{5}{9}(0)
Step 3: Calculate the result.
C=0C = 0
Step 4: Write the answer with the degree symbol and the scale letter, with no space between the number and °.
0°C0°\text{C}
Answer: 32°F equals 0°C.

Why It Matters

You will use the degree symbol every time you label angles in geometry, from elementary math through high-school trigonometry and beyond. It also appears constantly in science classes when recording temperatures and in geography when writing latitude and longitude coordinates like 40.7° N, 74.0° W.

Common Mistakes

Mistake: Putting a space between the number and the degree symbol (writing 90 ° instead of 90°).
Correction: The degree symbol should sit right against the number: 90°. Think of it like a tiny label glued to the digit.
Mistake: Leaving the degree symbol off entirely and just writing a number like 45 when you mean an angle.
Correction: Without the symbol, the reader cannot tell if you mean 45 degrees or 45 radians (or just the number 45). Always include ° for angles measured in degrees.
Mistake: Using a lowercase letter 'o' or a superscript zero instead of the real degree symbol.
Correction: These look similar but are different characters. Use the actual degree symbol (°) so your work is clear and professional. On most devices there is a shortcut or special-character menu to insert it.

Check Your Understanding

Write "a straight angle is 180 degrees" using the degree symbol correctly.
Hint: Place the small circle right after the number with no space.
Answer: A straight angle is 180°.
Which is written correctly: 25 °C, 25° C, or 25°C?
Hint: The degree symbol always touches the number.
Answer: 25°C is correct — no space between the number and the degree symbol.
Two angles are supplementary. One is 135°. Write the other angle with the degree symbol.
Hint: Supplementary angles add up to 180°.
Answer: 45°, because 180° − 135° = 45°.

Related Terms

  • DegreeThe unit of angle measurement the symbol represents
  • Integral SignAnother math symbol with its own reference page
  • Multiplication SignA common math operation symbol
  • Percent SignAnother symbol placed right after a number
  • CaretSymbol used to show exponents in typed math
  • TildeSymbol used in approximation and other math contexts
  • Plus or Minus (±)Another special math notation symbol