Decibels in ultrasonic testing: the 6 dB and 20 dB rules

The one formula

The decibel difference between two echo amplitudes is dB = 20 × log₁₀ (A2 / A1). Evident's UT materials give this form, and our formulas guide cites the pages. Going the other way, ratio = 10^(dB / 20).

The 20 is there because power scales with the square of amplitude. For echo height on the screen you use 20, not 10. If a question talks about energy or intensity instead, read it twice, because the factor can change.

Two shortcuts worth memorizing

You will not always have a log key handy, and you rarely need one.

Chain them. 12 dB is two doublings, so a factor of about 4 (exact: 3.98). 26 dB is 20 dB plus 6 dB, so about 10 × 2 = 20 (exact: 19.95). Shortcuts are close enough for a sanity check on a calculator answer.

Four worked examples

All numbers are invented for practice.

1. Gain to ratio. You add 14 dB of gain. What happens to a signal's height? Use the formula: 10^(14/20) = 5.01. The echo is about five times taller, before it hits the top of the screen.

2. Ratio to gain. An echo is at 20% screen height and you want it at 80%. The ratio is 4, so dB = 20 × log₁₀ (4) = 12.0 dB. Two doublings, which matches the shortcut.

3. Comparing two echoes. A reference echo reads 80% and a second one reads 32%. dB = 20 × log₁₀ (32 / 80) = 20 × log₁₀ (0.4) = -7.96 dB. The second echo is about 8 dB below the reference, so about 8 dB of added gain brings it to the same height.

4. Gain with a limit. An echo sits at 40% height. How much gain brings it to 100% full screen height? Ratio = 100 / 40 = 2.5. dB = 20 × log₁₀ (2.5) = 7.96 dB, or about 8 dB. Adding 14 dB instead would call for a ratio of 5.01, so the signal would reach 200%, which the screen cannot show. A clipped echo is no longer a measurement.

Sign mistakes and other traps

• Direction of the ratio. Some sources write 20 log (A1 / A2) and others 20 log (A2 / A1). The size is identical and only the sign flips. Decide what "positive" means in the question, then keep it.
• Mixing 10 and 20. Use 20 for amplitude. A student who uses 10 gets half the right dB, which is a classic wrong answer on a multiple-choice list.
• Reading past 100%. Gain math assumes the screen is linear and unclipped. Do not trust a ratio from a clipped echo.
• Adding ratios. Decibels add and ratios multiply. 6 dB + 6 dB = 12 dB, which is about ×4 in amplitude (2 × 2).
• Rounding too early. Carry three significant figures until the last step.

How this shows up in practice

Setting a reference level, comparing a flaw echo with a reference reflector and describing a distance-amplitude change are all decibel jobs. The DAC curve guide and the attenuation guide use the same arithmetic. Check your own numbers with the decibel calculator after you work each problem by hand.

Test the skill, then fix the gap

Decibel math is quick to learn and quick to forget. Take the free 10-question UT check and see whether it holds under a clock. It needs no signup and explains every answer. For repeated math drills and timed practice exams, see the plans. In the course, Echo, the AI study buddy, can explain a missed decibel question step by step.

FAQ

Why is 6 dB a doubling?

Because 20 × log₁₀ (2) is 6.02. The shortcut is rounded, which is fine for a check and not for a final answer when the question wants two decimals.

Is it 10 log or 20 log?

For amplitude ratios, such as echo height on the screen, it is 20 log. A factor of 10 log applies to power or intensity ratios. Read what the question compares.

What is a dB difference of zero?

The two amplitudes are equal. The ratio is 1 and log₁₀ (1) is 0.

Can the exam ask me to compute logs by hand?

Pearson VUE says a calculator is built into the exam software and that you should not bring your own. Our exam day guide covers the layout, so practice the keystrokes.

Sources

• Evident Scientific, Ultrasonic Transducers Technical Notes (decibel and amplitude ratio equation), as cited in our UT formulas guide.
• ASNT NDT Level II Examinations, ASNT Certification Services: UT General topics.
• Pearson VUE's ASNT page, Pearson VUE: the built-in exam calculator.