How to Calculate a DB Gain

Logarithms are used to calculate db gain.

Db gain, which stands for decibel gain, is the logarithm of the ratio of two numbers multiplied by 10. When a ratio is expressed as decibel gain, the ratio of two numbers is much smaller than just the ratio obtained by dividing two numbers. For example, the ratio of 200 to 2 is 100, but this ratio expressed as a logarithm is 2, and expressed as a db gain is 20. Engineers and scientists convert ratios to decibel gain because large numbers converted to db gain are easier to work with for making technical calculations.

Things You'll Need

• Scientific calculator

Instructions

1. Pick two very large numbers, one much smaller than the other. For this example, pick 1 billion for the large number and then pick 10 for the small number.

2. Calculate the ratio of the big number to the small number. Divide the larger number by the smaller number. For this example divide 1 billion by 10. Enter in your calculator 1,000,000,000,000 (one billion), press the divide symbol then enter in 10. Examine the result displayed on your calculator. Check to see if the number displayed is 100 million, that is a 1 followed by 8 zeros (100,000,000).

3. Calculate the logarithm of the ratio obtained in the previous step. Locate the logarithm button on your scientific calculator. Press it. Now enter in the ratio obtained in the previous step, 100,000,000. Examine the result on the calculator's display. Check to see if it reads 8. Conclude that 8 is the logarithm of 100,000,000.

4. Calculate the Db Gain. Multiply the logarithm of the ratio obtained in the previous step by 10. For this example, since the logarithm was 8, the result is 80, since 8 times 10 is 80. Conclude that the dB gain is 80.

Tips & Warnings

• Different scientific calculators may require that you enter in the numbers and operations in different order. You can also use a logarithm calculator, resource 1, to calculate the logarithm.

• Instead of 100,000,000 for the ratio, your calculator may display 1 E 08. This is 100,000,000 represented in scientific notation, a way that a calculator uses to express very large numbers.

• Db gain may be calculated differently for different applications. The procedure presented is used only when comparing ratios that involve watts, a unit of measurement of power. Most of the other procedures are variations of this procedure. Common to them all is the use of logarithms.

References

• Numericana: Final Answers, Gérard P. Michon, Ph.D.Scales and Ratings: Measuring without units -
• Gignac: Unit 5: Day 11: Solving Real World Problems Algebraically
• Clemson Vehicular Electronics Laboratory: Working with Decibels

Resources

• RechnerOnline: Calculate Logarithm
• LightMachinery: Percent to dB Conversion Calculator