Sound-pressure ladder and wave ratioLevel position, reference, and relative amplitudes
Unit Converters
Sound Level Reference Table Calculator
Calculate a sound-pressure level from an explicitly stated reference pressure, then build a reference table that shows why equal decibel steps do not represent equal pressure increments.
REFERENCED SOUND-PRESSURE LEVEL
Convert RMS pressure to a logarithmic level without losing the reference
Use this page to study the relationship between pascals, pressure ratio, intensity ratio, and decibels. The result is unweighted sound-pressure level only; it is not an exposure or hearing-risk assessment.
Reference convention: 20 µPa is commonly used for airborne sound pressure, but every reported decibel value must retain its quantity and reference. Both pressures must be positive.
Sound-pressure level—
Pressure ratio—
Intensity ratio—
Entered pressure—
Reference pressure—
Pressure decades—
LOGARITHMIC PRESSURE LADDER
See the decibel position and the ratio behind it
The upper ladder locates the current dB level on an even logarithmic scale. The lower waves compare relative pressure amplitudes, while the table states exact pressure and intensity ratios for standard level steps.
| Level change | Pressure | Pressure / reference | Intensity / current |
|---|
HOW TO USE
Report a level with its full identity
- Enter a positive RMS sound pressure in pascals from a defined measurement.
- Enter the reference pressure explicitly; use 20 µPa only when that convention applies.
- Read the dB result together with pressure and intensity ratios.
- Use the step table to compare logarithmic changes without adding raw pressures incorrectly.
- Record weighting, averaging, bandwidth, and measurement conditions outside this unweighted reference calculation.
LEVEL FUNDAMENTALS
Six concepts prevent decibel mistakes
CALCULATION METHOD
Use a field-quantity level for pressure
rp = p/p0Lp = 20 log10(rp)rI = rp² = 10^(Lp/10)p2/p1 = 10^(ΔL/20)
WHY THE FACTOR IS 20
Acoustic intensity is proportional to pressure squared under matched conditions
A power-quantity level uses 10 log10. Because pressure is a field quantity and intensity follows its square when impedance conditions match, substituting the pressure ratio produces 20 log10. Using 10 log10 for pressure would understate the level change by half.
REFERENCE IDENTITY
“80 dB” is incomplete without quantity and reference
The same numeric decibel value can describe sound pressure, sound power, voltage, gain, attenuation, or another ratio. A professional record names Lp, the reference pressure, weighting, frequency bandwidth, and averaging. This page places the reference directly in the result.
ADDITION AND AVERAGING
Independent levels cannot be added as ordinary numbers
To combine sources or average energy, convert levels to compatible linear power quantities, combine those quantities, then convert back. This reference page intentionally handles one pressure and one reference; it does not provide source summation or time averaging.
DETAILED CALCULATION PROCESS
Default 0.2 Pa substitution
| Symbol | Meaning | Default | Unit |
|---|---|---|---|
| p | RMS pressure | 0.2 | Pa |
| p0 | Reference pressure | 0.00002 | Pa |
| rp | Pressure ratio | calculated | dimensionless |
| Lp | Pressure level | calculated | dB re p0 |
- Confirm both p and p0 are positive RMS pressures.
- Pressure ratio = 0.2/0.00002 = 10,000.
- log10(10,000) = 4.
- Sound-pressure level = 20 × 4 = 80 dB re 20 µPa.
- Intensity ratio = 10,000² = 100,000,000.
- A +20 dB step multiplies pressure by 10.
- A +10 dB step multiplies pressure by 3.1623 and intensity by 10.
- Reverse check: 0.00002 × 10^(80/20) = 0.2 Pa.
RESULT INTERPRETATION
Equal decibel steps mean equal ratios, not equal pascal increments
Zero dB means pressure equals the reference, not absence of sound. Negative dB means pressure below the reference and is mathematically valid. Each +20 dB multiplies pressure by ten; each +10 dB multiplies intensity by ten. Perceived loudness is not calculated.
MEASUREMENT EVIDENCE
Keep acoustical conditions with the number
Retain microphone, calibration, position, orientation, bandwidth, frequency weighting, time weighting, averaging interval, RMS method, environment, background correction, source state, distance, reference quantity, timestamp, and uncertainty.
LIMITS AND EXCLUSIONS
What this logarithmic reference does not establish
- No A, C, or frequency weighting is applied.
- No exposure time, dose, or hearing-risk decision is calculated.
- No multiple-source addition or spatial averaging is performed.
- No loudness, annoyance, or audibility model is used.
- No regulatory or occupational limit is supplied.
WORKED DECISION CASES
Reference arithmetic supports different analyses
Microphone calibration check
A known RMS pressure is converted to a referenced level to confirm the logger’s scaling path. Weighting and calibrator certificate remain separate evidence.
Exposure question
An 80 dB unweighted pressure level is not enough to determine exposure. The analyst needs A-weighting, duration, temporal variation, measurement uncertainty, and the governing rule.
TECHNICAL GLOSSARY
Acoustical level terms
- Pascal
- SI unit of pressure.
- RMS
- Root-mean-square value over a defined interval.
- Reference quantity
- Positive denominator defining the level zero.
- Decibel
- Logarithmic unit equal to 0.1 bel.
- Sound-pressure level
- 20 log10 of pressure ratio.
- Frequency weighting
- Frequency-dependent response applied to a signal.
- Time weighting
- Specified detector response over time.
- Bandwidth
- Frequency interval represented by the measurement.
IMPORTANT NOTE
Do not use this unweighted result as an exposure decision
Exposure assessment requires the applicable weighting, duration, averaging, uncertainty, and governing rule. This page is a pressure-level reference only.
Frequently asked questions
Why must pressure be positive?
The logarithm requires a positive RMS magnitude.
Does 0 dB mean silence?
No. It means pressure equals the selected reference.
Can dB be negative?
Yes, when pressure is below the reference.
Why use 20 log10?
Pressure is a field quantity linked to squared intensity.
Does +6 dB double pressure?
Approximately; the exact factor is 10^(6/20).
Does +10 dB double loudness?
This calculator makes no loudness claim.
Can levels be added directly?
No. Convert to compatible linear quantities first.
Is this dBA?
No. No frequency weighting is applied.
AUTHORITATIVE BASIS
Logarithmic quantity conventions
- NIST Guide to the SI, Chapter 8 — logarithmic quantities, decibel, and explicit reference notation.
- NIST SP 330 Section 4.