EQ Converter - User Guide

Convert between Quality Factor (Q) and Bandwidth in Octaves

Overview

EQ Converter is a professional tool for audio engineers and sound designers that converts between Quality factor (Q) and bandwidth in octaves. It also calculates approximate −3 dB bandwidth in Hertz when a center frequency is provided.

Perfect for working with parametric equalizers, filters, and audio processing equipment that use different measurement systems.

Quick Start

  1. Select your conversion mode using the segmented control at the top:
    • Q → Bandwidth - Convert Quality factor to bandwidth in octaves
    • Bandwidth → Q - Convert bandwidth in octaves to Quality factor
  2. Enter your input value (Q or bandwidth depending on mode)
  3. Optionally enter a center frequency (f₀) in Hz to see the approximate −3 dB bandwidth
  4. Results update automatically as you type
  5. Tap the copy button on any result card to copy the value to your clipboard

Conversion Modes

Q → Bandwidth (Octaves)

Convert Quality factor to bandwidth in octaves:

  1. Select "Q → Bandwidth" mode
  2. Enter the Quality factor (Q) value
  3. The bandwidth in octaves is calculated and displayed
  4. If you enter a center frequency (f₀), the approximate −3 dB bandwidth in Hz is also shown

Q Range: Must be greater than 0 and less than or equal to 100

Bandwidth → Q

Convert bandwidth in octaves to Quality factor:

  1. Select "Bandwidth → Q" mode
  2. Enter the bandwidth in octaves
  3. The Quality factor (Q) is calculated and displayed
  4. If you enter a center frequency (f₀), the approximate −3 dB bandwidth in Hz is also shown

Bandwidth Range: Must be greater than 0 and less than or equal to 6 octaves

Understanding Q and Bandwidth

Quality Factor (Q)

Q is a dimensionless parameter that describes the sharpness of a filter or equalizer band:

  • High Q (e.g., Q = 10) = Narrow, sharp filter
  • Low Q (e.g., Q = 0.5) = Wide, gentle filter
  • Q is commonly used in parametric EQs and filter designs

Bandwidth in Octaves

Bandwidth describes how wide a filter is, measured in octaves:

  • Narrow bandwidth (e.g., 0.1 oct) = Sharp, focused filter
  • Wide bandwidth (e.g., 2 oct) = Broad, gentle filter
  • One octave = a doubling of frequency (e.g., 1 kHz to 2 kHz)

Relationship

Q and bandwidth are inversely related:

  • Higher Q = Narrower bandwidth
  • Lower Q = Wider bandwidth
  • The conversion uses standard DSP formulas for accuracy

Center Frequency (f₀)

The center frequency (f₀) is optional but useful for calculating the actual bandwidth in Hertz:

  • Enter the center frequency in Hz (e.g., 1000 for 1 kHz)
  • The app calculates the approximate −3 dB bandwidth in Hz
  • This shows the actual frequency range affected by the filter
  • Useful for understanding the real-world frequency impact

Example: If Q = 2 and f₀ = 1000 Hz, the bandwidth might be approximately 500 Hz (from 750 Hz to 1250 Hz).

Features

  • Two-Way Conversion - Convert in both directions instantly
  • Real-Time Updates - Results calculate automatically as you type
  • Input Validation - Red border and shake animation on invalid input
  • Range Warnings - Orange warning badges for values near limits
  • Copy to Clipboard - Tap any result card to copy the value
  • Haptic Feedback - Tactile confirmation when copying values
  • Persistent Values - Your inputs are saved and restored when you reopen the app
  • Clear Button - Quickly reset all fields from the toolbar
  • Dark Mode UI - Easy on the eyes for long sessions
  • Accessibility - Full VoiceOver support and Dynamic Type

Input Validation

Valid Ranges

  • Quality Factor (Q): Must be greater than 0 and ≤ 100
  • Bandwidth (oct): Must be greater than 0 and ≤ 6 octaves
  • Center Frequency (f₀): Must be a positive number

Invalid Input Handling

  • Invalid values show a red border around the input field
  • The field shakes to draw attention to the error
  • Results are not calculated until valid input is entered
  • Range warnings appear as orange badges for values near limits

Tips & Best Practices

For Audio Engineers

  • Use Q → Bandwidth when your EQ displays Q values and you need to know the bandwidth
  • Use Bandwidth → Q when your EQ displays bandwidth and you need the Q value
  • Enter the center frequency to see the actual frequency range affected
  • Copy results directly to your notes or DAW

Common Use Cases

  • Parametric EQ Settings: Convert between different EQ interfaces
  • Filter Design: Calculate Q values for specific bandwidth requirements
  • Audio Analysis: Understand the frequency range of filter settings
  • Equipment Matching: Match settings between different audio devices

Conversion Examples

Example 1: Q to Bandwidth

Input: Q = 2.0

Result: Bandwidth ≈ 0.67 octaves

This means a Q of 2 creates a filter that's about 2/3 of an octave wide.

Example 2: Bandwidth to Q

Input: Bandwidth = 1.0 octave

Result: Q ≈ 1.41

A 1-octave wide filter has a Q of approximately 1.41.

Example 3: With Center Frequency

Input: Q = 5.0, f₀ = 1000 Hz

Results:

  • Bandwidth ≈ 0.28 octaves
  • Approx. −3 dB bandwidth ≈ 200 Hz

At 1 kHz, a Q of 5 creates a narrow filter affecting roughly 200 Hz (from 900 Hz to 1100 Hz).

Example 4: Wide Filter

Input: Bandwidth = 2.0 octaves, f₀ = 500 Hz

Results:

  • Q ≈ 0.67
  • Approx. −3 dB bandwidth ≈ 750 Hz

A 2-octave wide filter at 500 Hz has a low Q and affects a wide frequency range.

Technical Details

  • Formulas: Uses standard DSP conversion formulas for accuracy
  • Precision: All calculations use double-precision floating point
  • Validation: Numerically stable algorithms prevent calculation errors
  • Platform: iOS 17+ (iPhone & iPad)
  • Localization: Number formatting uses your device's locale settings
  • Persistence: Values are saved using UserDefaults

Troubleshooting

Input shows red border and shakes?

  • Check that your value is within the valid range (Q: 0-100, Bandwidth: 0-6 octaves)
  • Ensure you're entering a valid number (no letters or special characters)
  • Make sure the value is positive (greater than 0)

No result displayed?

  • Enter a valid input value first
  • Check that the value is within the acceptable range
  • Try the Clear button and re-enter your values

Bandwidth in Hz not showing?

  • Enter a center frequency (f₀) value in Hz
  • The Hz calculation requires both bandwidth (or Q) and center frequency
  • Make sure f₀ is a positive number

Can't copy to clipboard?

  • Tap the copy button on the result card (not just the value)
  • You should feel haptic feedback when copying succeeds
  • Check that your device supports clipboard operations

Keyboard Shortcuts

  • Done Button: Appears in the keyboard toolbar to dismiss the keyboard
  • Clear Button: Located in the top-right toolbar to reset all fields
  • Mode Switch: Use the segmented control at the top to change conversion direction

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