RADIANS

Math & Trigonometry Functions
(4.7/5)

Converts degrees to radians. Multiply degrees by π/180 (approximately 0.01745329). Essential for trigonometric calculations, geometry, physics, engineering, and when working with angles in different measurement systems.

Interactive Formula Tester

=RADIANS("180")

Complete Theory & Understanding

Master the fundamentals of Excel RADIANS function

Core Concept

The RADIANS function converts angles from degrees to radians. The conversion factor is π/180 (approximately 0.01745329). This is essential when working with trigonometric functions (SIN, COS, TAN) which use radians, or when converting between measurement systems. Key conversions: 180° = π radians, 90° = π/2, 60° = π/3, 45° = π/4, 30° = π/6. RADIANS preserves the sign of the angle (negative degrees → negative radians).

Why Use RADIANS?

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

Key Characteristics

Conversion Factor

Multiplies by π/180

RADIANS(1) ≈ 0.01745

Preserves Sign

Negative degrees → negative radians

RADIANS(-90) ≈ -1.5708

Key Conversions

180° = π, 90° = π/2

RADIANS(180) = π

Complement to DEGREES

Inverse of DEGREES function

RADIANS(DEGREES(90)) = π/2

Function Anatomy

=RADIANS(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

=RADIANS(angle)
Required
angle:

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

Returns
Return Value:

The angle in radians

Description: Converts degrees to radians

Interactive Examples

Basic Conversion

Convert 180 degrees to radians

"180"
=RADIANS(180)
3.14159 (π)

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

VBA Implementation & Automation

Basic RADIANS in VBA

Use RADIANS function in VBA

' Basic RADIANS in VBA
Range("C1").Value = Application.WorksheetFunction.Radians(180)
' Returns: 3.14159 (π)

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

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

' Convert for trigonometry
Sub ConvertForTrigonometry()
    Dim degrees As Double
    degrees = Range("A1").Value
    Dim radians As Double
    radians = Application.WorksheetFunction.Radians(degrees)
    Dim sinValue As Double
    sinValue = Application.WorksheetFunction.Sin(radians)
    Range("B1").Value = sinValue
End Sub

Business Applications

Trigonometric Calculations

Convert angles for SIN, COS, TAN functions

=SIN(RADIANS(30))

Geometry Applications

Angle measurements and geometric calculations

=RADIANS(angle_degrees)

Physics & Engineering

Angle conversions in physics calculations

=RADIANS(degree_value)

Data Conversion

Converting between measurement systems

=RADIANS(cell_reference)

Common Issues & Solutions

#VALUE! Error

Non-numeric input in RADIANS

=RADIANS(VALUE(A1))

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

Wrong Conversion

Confusion between degrees and radians

Use DEGREES() to convert radians→degrees

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

Precision Issues

Small rounding differences

=ROUND(RADIANS(A1), 4)

Solution: Use known conversions: RADIANS(180) = π. For display, use ROUND: ROUND(RADIANS(angle), decimals).

Inverse Relationship

Confusion about RADIANS vs DEGREES

RADIANS converts degrees→radians

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

Performance Tips & Best Practices

⚡ Performance Optimization

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

🎯 Best Practices

  • Remember: 180 degrees = π radians
  • RADIANS converts FROM degrees TO radians
  • Use DEGREES() for opposite conversion
  • RADIANS preserves sign (negative stays negative)
  • Test with known values: RADIANS(180) = π
  • Document angle measurement units in formulas
  • Use RADIANS before trigonometric functions if input is in degrees