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DEGREES

Math & Trigonometry Functions
(4.7/5)

Converts radians to degrees. Multiply radians by 180/π (approximately 57.29577951). Essential for trigonometric calculations, geometry, physics, engineering, and when working with angles in different measurement systems.

Interactive Formula Tester

=DEGREES("3.14159")

Complete Theory & Understanding

Master the fundamentals of Excel DEGREES function

Core Concept

The DEGREES function converts angles from radians to degrees. The conversion factor is 180/π (approximately 57.29577951). This is essential when working with trigonometric functions (SIN, COS, TAN) which typically use radians, or when converting between measurement systems. Key conversions: π radians = 180°, π/2 = 90°, π/3 = 60°, π/4 = 45°, π/6 = 30°. DEGREES preserves the sign of the angle (negative radians → negative degrees).

Why Use DEGREES?

  • Convert angles for SIN, COS, TAN
  • Angle measurements and calculations
  • Angle conversions in calculations
  • Converting between measurement systems

Key Characteristics

Conversion Factor

Multiplies by 180/π

DEGREES(1) ≈ 57.2958

Preserves Sign

Negative radians → negative degrees

DEGREES(-1) ≈ -57.2958

Key Conversions

π = 180°, π/2 = 90°

DEGREES(PI()) = 180

Complement to RADIANS

Inverse of RADIANS function

DEGREES(RADIANS(90)) = 90

Function Anatomy

=DEGREES(parameters...)
Required
Parameters:

Function-specific parameters

Returns
Return Value:

Function-specific return type

Primary Use Cases

Trigonometry

Convert angles for SIN, COS, TAN

Geometry

Angle measurements and calculations

Physics & Engineering

Angle conversions in calculations

Data Conversion

Converting between measurement systems

Theory Summary

Precise

Exact matching required

Position-Based

Returns numeric position

Error-Safe

Handles missing text gracefully

Syntax & Parameters

=DEGREES(angle)
Required
angle:

The angle in radians that you want to convert to degrees.

Returns
Return Value:

The angle in degrees

Description: Converts radians to degrees

Interactive Examples

Basic Conversion

Convert π radians to degrees

"3.14159 (π)"
=DEGREES(3.14159)
180

Converts π radians to 180 degrees. DEGREES(π) = π × (180/π) = 180. This is the fundamental conversion: π radians = 180°.

VBA Implementation & Automation

Basic DEGREES in VBA

Use DEGREES function in VBA

' Basic DEGREES in VBA
Range("C1").Value = Application.WorksheetFunction.Degrees(3.14159)
' Returns: 180

' Convert radians to degrees
Sub ConvertRadiansToDegrees()
    Dim radians As Double
    radians = Range("A1").Value
    Dim degrees As Double
    degrees = Application.WorksheetFunction.Degrees(radians)
    Range("B1").Value = degrees
End Sub

' Convert multiple angles
Sub ConvertMultipleAngles()
    Dim i As Integer
    For i = 1 To 10
        Dim radians As Double
        radians = Range("A" & i).Value
        Dim degrees As Double
        degrees = Application.WorksheetFunction.Degrees(radians)
        Range("B" & i).Value = degrees
    Next i
End Sub

' Convert using PI
Sub ConvertPI()
    Dim pi As Double
    pi = Application.WorksheetFunction.Pi()
    Dim degrees As Double
    degrees = Application.WorksheetFunction.Degrees(pi)
    Range("B1").Value = degrees
    ' Returns: 180
End Sub

Business Applications

Trigonometric Calculations

Convert angles for SIN, COS, TAN functions

=DEGREES(RADIANS(45))

Geometry Applications

Angle measurements and geometric calculations

=DEGREES(angle_radians)

Physics & Engineering

Angle conversions in physics calculations

=DEGREES(radian_value)

Data Conversion

Converting between measurement systems

=DEGREES(cell_reference)

Common Issues & Solutions

#VALUE! Error

Non-numeric input in DEGREES

=DEGREES(VALUE(A1))

Solution: Ensure input is numeric. DEGREES requires a number. Check for text, errors, or empty cells. Use VALUE() if needed.

Wrong Conversion

Confusion between degrees and radians

Use RADIANS() to convert degrees→radians

Solution: DEGREES converts FROM radians TO degrees. If you have degrees and need radians, use RADIANS() instead. Remember: π rad = 180°.

Precision Issues

Small rounding differences

=ROUND(DEGREES(A1), 2)

Solution: Use PI() for exact values: DEGREES(PI()) = 180 exactly. For display, use ROUND: ROUND(DEGREES(angle), decimals).

Inverse Relationship

Confusion about DEGREES vs RADIANS

DEGREES converts radians→degrees

Solution: DEGREES and RADIANS are inverse: DEGREES(RADIANS(x)) = x and RADIANS(DEGREES(x)) = x. Use DEGREES when you have radians.

Related Functions

RADIANS

Converts degrees to radians

Math
SIN

Sine function (uses radians)

Math
COS

Cosine function (uses radians)

Math
TAN

Tangent function (uses radians)

Math
PI

Returns π constant

Math

Performance Tips & Best Practices

⚡ Performance Optimization

  • • DEGREES is fast - minimal performance impact
  • • Use PI() for exact conversions (DEGREES(PI()) = 180)
  • • DEGREES works efficiently in array formulas
  • • Avoid nested conversions (DEGREES(RADIANS(x)))
  • • Use cell references for multiple conversions

🎯 Best Practices

  • • Remember: π radians = 180 degrees
  • • DEGREES converts FROM radians TO degrees
  • • Use RADIANS() for opposite conversion
  • • DEGREES preserves sign (negative stays negative)
  • • Use PI() function for precision
  • • Test with known values: DEGREES(PI()) = 180
  • • Document angle measurement units in formulas