Degree Calculator
Use this tool to convert between angle formats and compute trig values from degrees.
Tip: 180° = π radians and π radians = 180°.
What Is a Deg Calculator?
A deg calculator is an angle tool that helps you work with degrees quickly and accurately. In mathematics, engineering, navigation, physics, GIS mapping, and even game development, angle units are used constantly. A reliable degree calculator saves time and reduces mistakes by handling common conversions and trigonometric computations in one place.
This page includes three practical tools: degree/radian conversion, decimal-degree and DMS conversion, and degree-based trig output.
What This Calculator Can Do
1) Degrees ↔ Radians
Most school-level geometry uses degrees, while higher math and programming often use radians. Converting between these units is one of the most frequent angle tasks.
- Degrees to radians: multiply by π/180
- Radians to degrees: multiply by 180/π
2) Decimal Degrees ↔ DMS
DMS means Degrees, Minutes, Seconds. It is widely used in surveying, astronomy, and geographic coordinates. Decimal degrees are often better for computation, while DMS is easier to read in field notes and maps.
- Decimal → DMS: split fractional parts into minutes and seconds
- DMS → Decimal: deg + min/60 + sec/3600 (apply sign)
3) Trig Values from Degrees
When you enter an angle in degrees, the calculator returns:
- sin(θ)
- cos(θ)
- tan(θ) (undefined when cos(θ)=0)
Core Formulas Used
- rad = deg × π/180
- deg = rad × 180/π
- decimal = sign × (D + M/60 + S/3600)
- DMS extraction: D = floor(abs(decimal)), M = floor(frac × 60), S = remaining × 60
Examples
Example A: Convert 225° to radians
225 × π/180 = 3.926990717 radians (approximately).
Example B: Convert 1.2 radians to degrees
1.2 × 180/π = 68.75493542° (approximately).
Example C: Convert -73.9857° to DMS
The value becomes approximately -73° 59′ 8.52″.
Where This Is Useful
- Trigonometry homework and exam checking
- CAD, robotics, and motion control
- GPS and geospatial coordinate formatting
- Data analysis scripts that expect radians
- Computer graphics and game rotations
Common Mistakes to Avoid
- Mixing degree-mode and radian-mode in calculators/software
- Using minutes/seconds values outside 0–59
- Forgetting sign on west/south or negative direction angles
- Expecting tan(90°) to be a finite number
Quick FAQ
Is 360° equal to 2π radians?
Yes. A full circle is 360°, which is exactly 2π radians.
Why does tan sometimes show as undefined?
Tangent is sin(θ)/cos(θ). When cos(θ) is zero (such as 90°, 270°), division is undefined.
When should I use decimal degrees instead of DMS?
Use decimal degrees for calculations and code. Use DMS when presenting coordinates for people to read.