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This page provides some formulae for general audio-related calculations, however for all calculations involving decibels see the Decibels page.

Below the general formulae on this page are calculators for these electrical calculations useful in audio work:


The symbols and units used in the formulae below are:


Ohm's Law
      V = IR       I = V / R     R = V / I

Series resistance
      Rtotal = R1 + R2 + R3 ...

Parallel resistance − calculators are available here
      Rtotal = 1  /  [(1 / R1) + (1 / R2) + (1 / R3) + ...]

Overall impedance of identical items (e.g. speakers) wired in parallel (typically, by daisy-chaining)
      Zoverall  =  Zone item   /  number of items

Resistive divider (unbalanced attenuator) − a calculator is available here
Rupper is the resistance connecting the input to the output.
Rlower is the resistance connecting the output to signal earth.
Zero source impedance and infinite load impedance are assumed.
      Vout = Vin Rlower  /   (Rlower + Rupper)

Reactance of capacitors and inductors
      XC  =  1  /  (2 π f C)       XL  =  2 π f L

3 dB cut-off frequency of simple RC filters − see these calculators
      f  =  1  /  (2 π R C)

Power (when voltage and current are DC or are in phase)
      P = IV       I = P / V     V = P / I
      P = V2 / R       V = sqrt(PR)     R = V2 / P
      P = I2R       I = sqrt(P / R)     R = P / I2

Apparent power
      VA = IV       I = VA / V     V = VA / I

Decibels (power ratios) − click here for value converters
      dB = 10 log10 (P / Pref)       P = Pref 10(dB / 10)  

Decibels (voltage ratios) − click here for value converters
      dB = 20 log10 (V / Vref)       V = Vref 10(dB / 20)  

Decibels (pressure ratios) − click here for value converters
      dB = 20 log10 (p / pref)       p = Vref 10(dB / 20)  

dBV & dBu − follow the links for information & value converters
      dBV = 20 log10 V       dBV = dBu − 2.2     V = 10(dBV / 20)
      dBu = 20 log10 (V / 0.775)       dBu = dBV + 2.2     V = 0.775 x 10(dBu / 20)

dB SPL − follow the link for information & value converter
      dB SPL = 20 log10 (p / 20E−6) p = 20E−6 x 10(dB SPL / 20) [20E−6 means 20 x 10−6]

Dynamic range (DR), signal-to-noise ratio (SNR) & headroom
of equipment (all in dB)
      DR = SNR + headroom       SNR = DR − headroom       headroom = DR − SNR

For microphone noise levels see Types of Noise Specification
on the Microphones page

Octaves
      number of octaves = 3.322 log10 (f / fref)

Velocity (speed) of sound in air
      v ≅ 331 + 0.6T

Propagation time
      t = d / v

Wavelength
      λ = v / f
      f = v / λ
    v = fλ

UK UHF channel number (N) and frequency
N.B. f here is in MHz.
   channel N starts at
        f = 8N + 302
   channel N ends at
        f = 8N + 310
      N = (f − 302) / 8
   ignore decimal part
When calculating N, if (f − 302) / 8 has no decimal part then f lies exactly
on the boundary between channels (N − 1) and N.

Parallel resistance calculator:

Use the first line for 2 resistances in parallel, OR the second line for 3 resistances in parallel.
Enter the known values in the relevant R1 / R2 / R3 boxes and click '=' to get the calculated value.
Use consistent units for each calculation − e.g. all ohms, all kilohms or all megohms.

R1:   parallel with R2:               
 
R1:   parallel with R2:   parallel with R3:        

Use the following calculator in the case where a second resistor will be connected in parallel with a known existing one, and it is required to determine what value this second resistor needs to be in order to give a required total resistance. In practice, as resistors come in standard values (see Tolerance), after using the calculator below the second resistor will need to be selected as being the closest available value. The calculator above can then be used to determine the actual total value that would be obtained using that value.
Enter the required total value and the known resistor's value in the Total and R1 boxes respectively, and click '=' to get the calculated second resistor value.
The Total value entered must be less than the R1 value. Use consistent units for each calculation − e.g. all ohms, all kilohms or all megohms.

Total:   R1:    Requires parallel R2             


Resistive divider calculator:

This gives the output voltage of an unbalanced resistive divider (attenuator), for a given input voltage. The change of level in dB (see Loss) is also calculated.
Enter the known values in the three left-most boxes and click '=' to get the calculated values. (If you are only interested in the dB loss then enter any random value for V in.)
'Upper R' is the resistance connecting the input to the output. 'Lower R' is the resistance connecting the output to signal earth.
This calculator assumes a zero source impedance and infinite load impedance. In the case of a resistive source impedance, first add its value to the upper resistor value. In the case of a resistive load impedance, first calculate the parallel value of that impedance and the lower resistor value (see the previous calculator).
Use consistent resistance units for each calculation − e.g. both ohms, both kilohms or both megohms.

        V out   
Upper R:   Lower R:   V in:          
        dB 

Balanced attenuators employ identical-value series resistors in each leg, followed by a parallel resistor between the two legs. For these attenuators, enter twice the value of each single series resistor in 'Upper R' and the actual value of the parallel resistor in 'Lower R'.

Series capacitor low-cut calculators:

These are calculators for simple series-capacitor low-cut filters, such as are formed by a coupling capacitor at the input or output of an amplifier, or between an amplifier's internal stages. They are accurate only when both the source impedance and the load impedance are purely resistive.
Enter the known values in the left-most boxes and click '=' to get the calculated value(s).
'Source R' is the resistive source impedance feeding the filter, including any intentional series resistance, in ohms. 'Load R' is the resistive load impedance being fed from the filter, including any intentional parallel resistance, in ohms. 'C' is the value of the capacitor in F (microfarads). 'f' is the frequency in Hz.

This calculates the cut-off frequency. The frequency calculated is that at which the level into the specified load has fallen by 3 dB from the level obtained at frequencies well above the cut-off frequency.

Source R:   Load R:   C:        Hz    

This calculates the loss in dB at a given frequency. Two values are calculated. The 'relative loss' is the loss provided by the filtering action alone − i.e. the additional loss relative to that obtained at frequencies well above the cut-off frequency. The 'total loss' figure includes the basic loss introduced by the attenuating effect of the resistive source and load impedances. (Remember that units are ohms, F and Hz.)

        dB relative
Source R:   Load R:   C:    f:      (loss)   
        dB total


Parallel capacitor high-cut calculators:

These are calculators for simple parallel-capacitor high-cut filters, such as are often used to form a basic RF filter at the input of an amplifier, or by unintentional cable capacitances. They are accurate only when both the source impedance and the load impedance are purely resistive.
Enter the known values in the left-most boxes and click '=' to get the calculated value(s).
'Source R' is the resistive source impedance feeding the filter, including any intentional series resistance, in ohms. 'Load R' is the resistive load impedance being fed from the filter, including any intentional parallel resistance, in ohms. 'C' is the value of the capacitor in F (microfarads). 'f' is the frequency in Hz.
This calculates the cut-off frequency. The frequency calculated is that at which the level into the specified load has fallen by 3 dB from the level obtained at frequencies well below the cut-off frequency.

Source R:   Load R:   C:        Hz    

This calculates the loss in dB at a given frequency. Two values are calculated. The 'relative loss' is the loss provided by the filtering action alone − i.e. the additional loss relative to that obtained at frequencies well below the cut-off frequency. The 'total loss' figure includes the basic loss introduced by the attenuating effect of the resistive source and load impedances. (Remember that units are ohms, F and Hz.)

        dB relative
Source R:   Load R:   C:    f:      (loss)   
        dB total


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This page last updated 25-Jun-2019.