dB Per Decade Calculator

Formula

The formula to calculate the dB per decade is:

\[ \text{dB/Decade} = \frac{\text{Final Level} - \text{Initial Level}}{\log_{10}(\frac{\text{Final Frequency}}{\text{Initial Frequency}})} \]

Where:

Initial Frequency (Hz) – The starting frequency of the signal.
Final Frequency (Hz) – The ending frequency of the signal.
Initial Level (dB) – The sound or signal level at the initial frequency.
Final Level (dB) – The sound or signal level at the final frequency.

What is dB Per Decade?

dB per decade is a measure of how much the level of a signal or sound changes over a tenfold increase in frequency. It is commonly used in audio engineering, electronics, and acoustics to describe the behavior of filters, amplifiers, and other frequency-dependent systems. A positive dB per decade indicates an increase in level with frequency, while a negative value indicates a decrease.

Example

For example, if the initial frequency is 100 Hz, the final frequency is 1000 Hz, the initial level is 20 dB, and the final level is 40 dB, the dB per decade can be calculated as follows:

\[ \text{dB/Decade} = \frac{40 - 20}{\log_{10}(\frac{1000}{100})} = \frac{20}{\log_{10}(10)} = \frac{20}{1} = 20 \]

So, the dB per decade for these values is 20.

10 dB/Decade

Formula: \( \text{Gain (dB)} = 10 \log_{10} \left( \frac{f_2}{f_1} \right) \)

Gain (dB): Gain in decibels
\( f_2 \): Higher frequency
\( f_1 \): Lower frequency

Example: \( \text{Gain (dB)} = 10 \log_{10} \left( \frac{1000}{100} \right) \)

Decades to Years Calculator

Formula: \( \text{Years} = \text{Decades} \times 10 \)

Years: Total number of years
Decades: Total number of decades

Example: \( \text{Years} = 3 \times 10 \)

dB per Octave to dB per Decade

Formula: \( \text{dB/Decade} = \text{dB/Octave} \times 3.32 \)

dB/Decade: Decibels per decade
dB/Octave: Decibels per octave

Example: \( \text{dB/Decade} = 6 \times 3.32 \)

How to Calculate Decades

Formula: \( \text{Decades} = \frac{\text{Years}}{10} \)

Decades: Total number of decades
Years: Total number of years

Example: \( \text{Decades} = \frac{50}{10} \)

20 dB/Decade

Formula: \( \text{Gain (dB)} = 20 \log_{10} \left( \frac{f_2}{f_1} \right) \)

Gain (dB): Gain in decibels
\( f_2 \): Higher frequency
\( f_1 \): Lower frequency

Example: \( \text{Gain (dB)} = 20 \log_{10} \left( \frac{2000}{200} \right) \)

40 dB/Decade

Formula: \( \text{Gain (dB)} = 40 \log_{10} \left( \frac{f_2}{f_1} \right) \)

Gain (dB): Gain in decibels
\( f_2 \): Higher frequency
\( f_1 \): Lower frequency

Example: \( \text{Gain (dB)} = 40 \log_{10} \left( \frac{3000}{300} \right) \)

dB per Decade in Octave

Formula: \( \text{dB/Octave} = \frac{\text{dB/Decade}}{3.32} \)

dB/Octave: Decibels per octave
dB/Decade: Decibels per decade

Example: \( \text{dB/Octave} = \frac{30}{3.32} \)

How Many Minutes in a Decade Calculator

Formula: \( \text{Minutes} = \text{Decades} \times 10 \times 365 \times 24 \times 60 \)

Minutes: Total number of minutes
Decades: Total number of decades

Example: \( \text{Minutes} = 1 \times 10 \times 365 \times 24 \times 60 \)

How to Calculate dB

Formula: \( \text{dB} = 10 \log_{10} \left( \frac{P_2}{P_1} \right) \)

dB: Decibels
\( P_2 \): Power level 2
\( P_1 \): Power level 1

Example: \( \text{dB} = 10 \log_{10} \left( \frac{100}{10} \right) \)

How Much is a Decade in Years

Formula: \( \text{Years} = \text{Decades} \times 10 \)

Years: Total number of years
Decades: Total number of decades

Example: \( \text{Years} = 2 \times 10 \)