Decibel Calculator
Convert between power ratios and decibel values. Uses dB = 10 × log₁₀(P₂/P₁) for power and dB = 20 × log₁₀(V₂/V₁) for voltage/amplitude. Also shows common sound level references.
The decibel (dB) is a logarithmic unit used to express the ratio between two values, most commonly for sound intensity, electrical power, and signal-to-noise levels. Originally derived from the "bel" (named after Alexander Graham Bell), the deci-bel is one-tenth of a bel and has become the standard unit for any quantity that spans many orders of magnitude.
Logarithmic scales matter because human perception works that way. Our ears, eyes, and other senses respond roughly to ratios, not absolute differences — the loudness difference between 60 and 70 dB feels similar to the difference between 80 and 90 dB. Decibels also tame astronomically large dynamic ranges. Audible sound spans from 10⁻¹² W/m² (threshold of hearing) to 10² W/m² (instant damage) — a factor of 10¹⁴. In decibels, that's just 0 to 140 dB, an intuitive range.
The basic formula for power is dB = 10 × log₁₀(P₂/P₁). For amplitude (voltage, sound pressure), it's 20 × log₁₀ because power is proportional to amplitude squared. A few useful benchmarks: +3 dB ≈ 2× power, +10 dB = 10× power, +20 dB = 100× power, +6 dB = 2× amplitude. Every doubling adds 3 dB of power or 6 dB of amplitude.
Common applications: sound level metering (occupational safety, environmental noise), audio engineering (signal levels, mixing), radio communications (link budgets), electronics (signal-to-noise ratios), and any field measuring ratios across many orders of magnitude.
Inputs
Results
Decibels
10.00 dB
Ratio
10.0000
Decibel Results
| Parameter | Value |
|---|---|
| Mode | Power Ratio → dB |
| Reference Power (P₁) | 1 |
| Measured Power (P₂) | 10 |
| Power Ratio | 10.000000 |
| Decibels | 10.0000 dB |
| Formula | dB = 10 × log₁₀(P₂/P₁) |
Formula
How to use this calculator
- Select the mode: power ratio → dB, amplitude ratio → dB, or dB → power ratio.
- Enter reference value (P₁ or V₁) — what you compare against.
- Enter measured value (P₂ or V₂) or the dB value to invert.
- Calculator returns dB or absolute ratio.
- For sound: 0 dB SPL is threshold (20 μPa), normal speech ~60 dB.
- Remember: doubling distance from a point source drops sound by 6 dB.
Worked examples
Amplifier gain
**Scenario:** A microphone outputs 1 mV; an amplifier outputs 1 V to the speaker. Gain? **Calculation:** Voltage ratio: 1 V / 0.001 V = 1000. dB = 20 × log(1000) = 60 dB. **Result:** 60 dB voltage gain (or 30 dB if measured in power, since 60 dB amplitude = 60 dB power for the same impedance). Typical mic-preamp combo gain.
Concert exposure time
**Scenario:** Rock concert peaks at 110 dBA. How long can you safely listen per OSHA? **Calculation:** OSHA halves allowed time per 5 dB above 90: 8 hr → 4 hr → 2 hr → 1 hr → 30 min at 110 dB. **Result:** Maximum ~30 minutes without hearing protection. Multi-hour concerts at 110+ dB cause measurable hearing damage. Earplugs (typical −15 to −25 dB attenuation) bring effective exposure down to safer levels.
Reducing road noise
**Scenario:** Highway sound is 75 dB at 10 m. Approximate level at 100 m (in free field)? **Calculation:** Doubling distance drops by 6 dB. From 10 m to 100 m is ~3.3 doublings. Drop: 3.3 × 6 ≈ 20 dB. **Result:** ~55 dB at 100 m — about quiet conversation. Real-world includes ground reflection, foliage, walls, and atmospheric absorption. Sound barriers add typically 10-15 dB reduction.
When to use this calculator
**Use decibel calculations for:**
- **Sound measurement**: environmental, occupational, acoustic. - **Audio engineering**: signal levels, gain staging, headroom. - **Radio communications**: link budgets, antenna gain. - **Electronics**: amplifier gain, SNR, dynamic range. - **Hearing safety**: OSHA, NIOSH exposure limits. - **Loudspeaker specifications**: efficiency, max SPL. - **Mixing and mastering**: digital level management. - **Telecom**: cable loss, repeater spacing.
**Why decibels:**
- **Compression**: huge dynamic ranges fit in small numbers. - **Perception**: matches how senses respond (logarithmic). - **Addition for cascaded gain**: amplifier gains stack additively (30 dB + 20 dB = 50 dB). - **Universality**: works for any ratio, not just sound.
**Reading dB notation:**
- **Bare "dB"**: relative ratio, no absolute reference. - **dBm**: relative to 1 mW (common in RF). - **dBW**: relative to 1 W. - **dB SPL**: sound pressure level relative to 20 μPa. - **dBA, dBC**: weighted SPL. - **dBFS**: digital level relative to full scale (always negative or 0). - **dBV**: voltage relative to 1 V. - **dBu**: voltage relative to 0.775 V.
**Combining sound sources:**
Two equal noise sources: +3 dB (not +6, not 2×). Reason: power adds (since they're incoherent), and 10×log(2) = 3. Doubling sources adds 3 dB each time.
**Distance effects (free field):**
- Point source: −6 dB per doubling. - Line source (road): −3 dB per doubling. - Plane source (large factory wall): no drop.
**Common applications:**
- **Workplace safety**: OSHA noise dosimetry (8-hr time-weighted average). - **Aviation**: aircraft noise certification (EPNdB). - **Construction**: equipment noise specs. - **Recording studios**: microphone preamp gain settings. - **Live sound**: mixer faders typically in dB. - **Network engineering**: cable attenuation (dB/km). - **Photonics**: optical fiber loss (dB/km).
**Software:**
- **REW (Room EQ Wizard)**: free acoustic measurement. - **Smaart, EASE**: pro acoustic analysis. - **MATLAB**: signal processing. - **SLM apps**: smartphone sound level meters (approximate).
**Common pitfalls:**
- **Power vs amplitude formula**: 10× log vs 20× log. - **Reference confusion**: dBm vs dBW vs dBFS. - **Weighting omitted**: 85 dB (unweighted) ≠ 85 dBA. - **Adding linearly**: 70 dB + 70 dB ≠ 140 dB; it's 73 dB. - **Free-field assumption**: indoor/reverberant rooms behave differently. - **Confusing perceived loudness with dB**: 10 dB increase = ~2× perceived loudness, not 10×.
**Perceived loudness:**
- +3 dB: just barely noticeable. - +10 dB: roughly twice as loud (perceptual). - −10 dB: roughly half as loud.
The phon and sone scales attempt perceptual loudness but are more complex.
Common mistakes to avoid
- Using 10× log for amplitude instead of 20× log.
- Adding dB linearly (90 + 90 dB ≠ 180 dB; it's 93 dB).
- Confusing dB references (dBm vs dBW vs dB SPL).
- Omitting weighting (dB vs dBA can differ by 10+ dB at low frequencies).
- Assuming dB scale is linear in loudness perception.
- Using free-field distance law in reverberant rooms.
- Reporting peak when average is needed (or vice versa).
- Forgetting that 0 dB is a reference, not silence.