Calculator with Degrees Symbol

The degrees symbol (°) is a common notation used in various scientific and everyday contexts. This calculator helps you work with degrees in temperature conversion and angle measurements.

What is the Degrees Symbol?

The degrees symbol (°) is used to indicate an angle measurement or a temperature value. It's a dimensionless unit that represents a fraction of a full rotation (360°) or a point on a temperature scale.

The degrees symbol is distinct from the degree symbol (°) used in temperature measurements. While both use the same symbol, they represent different quantities.

In temperature measurements, degrees can refer to Celsius (°C), Fahrenheit (°F), or Kelvin (K). In angle measurements, degrees are used to quantify the size of an angle in a circle.

Temperature Conversion

Temperature conversion between Celsius, Fahrenheit, and Kelvin is a common use of the degrees symbol. The formulas for these conversions are:

Celsius to Fahrenheit: °F = (°C × 9/5) + 32

Fahrenheit to Celsius: °C = (°F - 32) × 5/9

Celsius to Kelvin: K = °C + 273.15

Kelvin to Celsius: °C = K - 273.15

For example, 25°C is equivalent to 77°F and 298.15 K. These conversions are essential in scientific research, weather forecasting, and everyday life.

Example Conversion

Let's convert 100°F to Celsius:

°C = (100 - 32) × 5/9 = 37.78°C

So, 100°F is approximately 37.78°C.

Angle Measurements

In geometry and trigonometry, the degrees symbol is used to measure angles. A full circle is 360°, with each degree representing 1/360 of a full rotation.

Radians are another unit for angle measurement, where π radians equals 180°. The conversion between degrees and radians is important in advanced mathematics and physics.

Common angle measurements include:

Acute angle: 0° to 90°
Right angle: 90°
Obtuse angle: 90° to 180°
Straight angle: 180°
Reflex angle: 180° to 360°

Angle Conversion Example

Convert 45° to radians:

Radians = Degrees × (π/180) = 45 × (π/180) ≈ 0.785 radians

Common Uses

The degrees symbol appears in various fields:

Field	Common Uses
Science	Temperature scales, angle measurements, and trigonometric functions
Engineering	Design specifications, structural analysis, and mechanical systems
Everyday Life	Weather reports, cooking, and navigation
Mathematics	Geometry, trigonometry, and calculus problems

Understanding the degrees symbol is essential for accurate measurements and calculations across these disciplines.

FAQ

What is the difference between °C and °F?

°C (Celsius) and °F (Fahrenheit) are temperature scales. °C is used in most countries, while °F is primarily used in the United States. The freezing point of water is 0°C (32°F) and the boiling point is 100°C (212°F).

How do I convert degrees to radians?

To convert degrees to radians, multiply the degree value by π/180. For example, 90° × (π/180) = π/2 radians.

What is absolute zero in Kelvin?

Absolute zero is 0 K (-273.15°C or -459.67°F), the lowest possible temperature where molecular motion ceases.

Can I use the degrees symbol for slope measurements?

Yes, the degrees symbol is used to measure slope angles in construction and civil engineering. A 10° slope means the ground rises 1 unit vertically for every 5.73 units horizontally.