Convert kHz or Hz to a dB-style index, 20 × log10(f ÷ 1 kHz), or a dB value back to frequency. Frequency alone cannot give a real sound level.
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Frequency-Ratio Index Formula
The following formula defines a mathematical frequency-ratio index on the 20-log scale. The calculator also offers a 10-log scale; neither choice establishes a physical sound or gain level.
Variables:
- I is the defined logarithmic frequency-ratio index; k is the selected mathematical scale factor
- f is the input frequency
- fref is the reference frequency
To calculate this index, divide frequency by reference frequency, take its base-10 logarithm and multiply by the selected factor, 20 or 10.
What is kHz to dB?
Frequency and level are different quantities. This tool applies a defined logarithmic scale to f/f₀; it does not infer amplitude, power, sound pressure or gain. A physical 20-log interpretation would require a separately established amplitude ratio A/A₀ = f/f₀; a 10-log interpretation would require P/P₀ = f/f₀. Frequency measurements alone do not establish either relationship.
On the defined 20-log scale, equal frequencies give index 0, doubling gives about +6.02, halving gives about −6.02, and a tenfold ratio gives +20. The 10-log index is half as large for the same frequency ratio. Zero means equal frequencies, not silence.
How to Calculate the Frequency-Ratio Index?
The following steps calculate the mathematical index from a frequency ratio.
- First, determine the input frequency in kilohertz (f).
- Next, determine the reference frequency in kilohertz (fref).
- Divide the input frequency by the reference frequency to find the ratio.
- Choose the scale and apply I = k·log10(f / fref), where k is 20 or 10.
- After calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
Frequency (f) = 2 kHz
Reference Frequency (fref) = 1 kHz
20-log index I = 20·log10(2 / 1) ≈ 6.02
Frequency-Ratio Index Table (20-log Scale, Relative to 1 kHz)
The table lists the defined 20-log frequency-ratio index relative to 1 kHz. These values do not measure sound level or gain.
| Frequency (kHz) | Reference (kHz) | 20-log index |
|---|---|---|
| 0.25 | 1 | -12.04 |
| 0.5 | 1 | -6.02 |
| 1 | 1 | 0.00 |
| 2 | 1 | +6.02 |
| 5 | 1 | +13.98 |
| 10 | 1 | +20.00 |
The mathematical index can compare frequencies on a chosen logarithmic scale. Octaves provide a conventional frequency comparison: log₂(f/f₀). Acoustic level or device gain needs additional amplitude, power or response data and the appropriate reference; no universal frequency-to-level conversion exists.
