Audio Engineering Formulas
Audio engineering formulas relate level, frequency, and impedance across amplifiers, crossovers, and loudspeakers. These calculators help you match levels and design crossover networks accurately. They are essential for hi-fi, pro audio, and instrument design.
Audio Engineering Formula Calculators
- Audio Crossover Frequency f_c = 1 / (2π√(LC)) Inductance 100 µH, Capacitance 100 nF → Crossover Frequency = 50.33 kHz
- SPL from Power & Sensitivity SPL = sensitivity + 10 × log₁₀(P) Speaker Sensitivity 0.66 dB, Power 10 mW → Sound Pressure Level = -19.34 dB
- Audio Cable High-Frequency Rolloff f_3dB = 1 / (2πRC) Source Impedance 1 Ω, Cable Capacitance 1 pF → Rolloff Frequency = 159.2 GHz
- SPL from Pressure SPL = 20 × log₁₀(p / p_ref) Sound Pressure 10 Pa → Sound Pressure Level = 114 dB
- Crest Factor CF = V_peak / V_rms Peak Voltage 0.33 V, RMS Voltage 0.726 V → Crest Factor = 0.4545
- Reverberation Time (RT60) RT60 = 0.161 × V / (α × S) Room Volume 1 × 10⁻⁴ m³, Avg Absorption Coeff 0.025, Total Surface Area 1 × 10⁻⁵ m² → Reverb Time = 1.073 min
- Total Harmonic Distortion THD = √(V₂²+V₃²+V₄²+V₅²) / V₁ × 100% Fundamental (V₁) 0.33 V, 2nd Harmonic (V₂) 0.726 V, 3rd Harmonic (V₃) 1.55 V, 4th Harmonic (V₄) 155 mV, 5th Harmonic (V₅) 3.3 V → THD = 1127 %
Worked result for every Audio Engineering formula
| Formula | Expression | Worked result |
|---|---|---|
| Audio Crossover Frequency | f_c = 1 / (2π√(LC)) | Inductance 100 µH, Capacitance 100 nF → Crossover Frequency = 50.33 kHz |
| SPL from Power & Sensitivity | SPL = sensitivity + 10 × log₁₀(P) | Speaker Sensitivity 0.66 dB, Power 10 mW → Sound Pressure Level = -19.34 dB |
| Audio Cable High-Frequency Rolloff | f_3dB = 1 / (2πRC) | Source Impedance 1 Ω, Cable Capacitance 1 pF → Rolloff Frequency = 159.2 GHz |
| SPL from Pressure | SPL = 20 × log₁₀(p / p_ref) | Sound Pressure 10 Pa → Sound Pressure Level = 114 dB |
| Crest Factor | CF = V_peak / V_rms | Peak Voltage 0.33 V, RMS Voltage 0.726 V → Crest Factor = 0.4545 |
| Reverberation Time (RT60) | RT60 = 0.161 × V / (α × S) | Room Volume 1 × 10⁻⁴ m³, Avg Absorption Coeff 0.025, Total Surface Area 1 × 10⁻⁵ m² → Reverb Time = 1.073 min |
| Total Harmonic Distortion | THD = √(V₂²+V₃²+V₄²+V₅²) / V₁ × 100% | Fundamental (V₁) 0.33 V, 2nd Harmonic (V₂) 0.726 V, 3rd Harmonic (V₃) 1.55 V, 4th Harmonic (V₄) 155 mV, 5th Harmonic (V₅) 3.3 V → THD = 1127 % |
Variables used across Audio Engineering formulas
- f_c — Crossover frequency (Hz)
- L — Inductor value (H)
- C — Capacitor value (F)
- SPL — Sound pressure level at 1 meter (dB SPL)
- sensitivity — Speaker sensitivity rating (dB SPL/1W/1m)
- P — Electrical power applied to the speaker (W)
- f — -3 dB rolloff frequency (Hz)
- R — Source output impedance (Ω)
- p — RMS sound pressure (Pa)
- CF — Crest factor (dimensionless ratio)
- V_peak — Peak voltage (V)
- V_rms — RMS voltage (V)
- RT60 — Reverberation time for 60 dB decay (s)
- V — Room volume (m³)
- α — Average absorption coefficient (0-1, dimensionless)
- S — Total surface area of the room (m²)
- THD — Total harmonic distortion (ratio, displayed as %)
- V₁ — Fundamental amplitude (V)
- V₂ through V₅ — Harmonic amplitudes (V)
Questions people ask about Audio Engineering
- Sensitivity power rating spl — SPL from Power & Sensitivity
Related Formula Categories
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