Example data
| Input | Normalized ratio (R) | Power dB (10·log10 R) | Amplitude dB (20·log10 R) | Typical interpretation |
|---|---|---|---|---|
| 0.5 | 0.5 | -3.0103 dB | -6.0206 dB | Half power, ~0.707 amplitude |
| 1 | 1 | 0.0000 dB | 0.0000 dB | No change |
| 2 | 2 | 3.0103 dB | 6.0206 dB | Double power, ~1.414 amplitude |
| 10 | 10 | 10.0000 dB | 20.0000 dB | Ten times power |
| 3:1 | 3 | 4.7712 dB | 9.5424 dB | Moderate gain |
| 150% | 1.5 | 1.7609 dB | 3.5218 dB | Small gain |
Formula used
Decibels express ratios on a logarithmic scale using base‑10 logs.
First, convert your input into a normalized ratio R.
- Power ratio:
dB = 10 · log10(R) - Amplitude / Voltage / Current ratio:
dB = 20 · log10(R)
The 20 factor applies because power is proportional to the square of amplitude. Use the mode that matches the physical quantity you are comparing.
How to use this calculator
- Select an input format: linear ratio, A:B, or percent.
- Enter your ratio values, then choose the measurement type.
- Enable invert if you need the reciprocal ratio.
- Press Calculate to view results above the form.
- Use the download buttons to save CSV or PDF.
This short article explains common decibel use-cases and quick checks for ratio conversions.
1) Why decibels are used
Decibels compress very large ratio ranges into manageable numbers. A power ratio of 1,000,000:1 becomes 60 dB, which is easier to compare across systems. This is why dB appears in audio meters, RF link budgets, amplifier specs, and optical measurements.
2) Power versus amplitude interpretation
Use 10·log10(R) when R is a power ratio (watts, milliwatts, energy per unit time). Use 20·log10(R) when R is an amplitude ratio (voltage, current, sound pressure). The 20 factor comes from power being proportional to amplitude squared.
3) Common benchmark ratios
A ratio of 2 gives +3.0103 dB in power mode and +6.0206 dB in amplitude mode. A ratio of 10 is +10 dB (power) or +20 dB (amplitude). These two anchors make quick mental checks easy during design and testing.
4) Reading negative dB correctly
When the ratio is below 1, the log is negative, so dB indicates attenuation. For example, 0.5 is -3.0103 dB (power) or -6.0206 dB (amplitude). In RF, negative dB often describes filter insertion loss; in audio, it may represent gain reduction or fader cuts.
5) Audio gain staging and headroom
Audio workflows routinely use dB for consistent scaling across devices. A 6 dB boost in amplitude mode doubles voltage, which can also halve available headroom if the next stage clips. Keeping track of dB helps balance noise floor, dynamic range, and perceived loudness without juggling raw ratios.
6) RF and instrumentation examples
In RF chains, you may multiply linear gains, but you add them in dB. A preamp of 15 dB followed by a cable loss of 2 dB nets 13 dB overall. The same idea is used for SNR: if the signal improves by 3 dB, the power doubles relative to noise.
7) Percent and A:B inputs for field work
Technicians often see ratios written as A:B or as percent change. Converting 150% to a ratio of 1.5 and then to dB provides a clear “how much” metric. Likewise, a compressor ratio like 3:1 can be treated as a simple ratio before conversion, depending on what you are analyzing.
8) Fast sanity checks
Use these rules to verify results: doubling power is about +3 dB, doubling amplitude is about +6 dB, and every 10× increase in power is +10 dB. If your output violates these benchmarks, recheck whether you selected the correct mode and whether the ratio should be inverted.
FAQs
1) Which mode should I choose?
Use power mode for watts and power measurements. Use amplitude mode for voltage, current, pressure, and other field quantities. If you are unsure, check whether your ratio directly represents power or an amplitude.
2) Why is 0 dB important?
0 dB means the ratio equals 1, so there is no gain or loss. It is a reference point that makes it easy to express increases as positive dB and decreases as negative dB.
3) What does -3 dB mean in power terms?
-3 dB is approximately half the power. More precisely, a power ratio of 0.5 equals -3.0103 dB. It is commonly used for half‑power points and bandwidth definitions.
4) What does +6 dB mean in amplitude terms?
+6 dB is approximately double the amplitude. More precisely, an amplitude ratio of 2 equals +6.0206 dB. In many audio contexts, this is a noticeable increase in level.
5) Why does the calculator reject zero or negative ratios?
The logarithm of zero is undefined, and negative ratios are not valid for log10 in this context. Ratios must be greater than 0 to compute dB reliably.
6) When should I use the invert option?
Use invert when your ratio is flipped. For example, if you typed output/input but need input/output, inversion corrects the direction. It is also useful when converting “loss” ratios into an equivalent gain form.
7) How many decimals should I keep?
For quick work, 1–2 decimals is usually fine. For engineering documentation, 3–6 decimals can help with reproducibility. The calculator shows higher precision so you can round appropriately for your use case.