Decibel (dB) Sum Calculator
Sound pressure level (SPL) is on a logarithmic scale — you cannot just add the numbers. Two 80 dB sources do not give 160 dB; they give about 83 dB. Four equal 80 dB sources give about 86 dB. And if one source is more than 10 dB above the rest, the quieter ones become essentially invisible. This tool applies the standard formula L_total = 10·log₁₀(Σ 10^(Lᵢ/10)) live as you type, breaks the result into "loudest source + everything else," and offers a second card that subtracts a background-noise floor from a measured total to recover the pure signal.
Combined sound pressure level
83.01
dB
—
Breakdown
- Loudest source
- —
- Gain over loudest
- —
- All others combined
- —
- Gain if N equal sources
- —
Subtract background noise (extract pure signal)
Measured total SPL minus background noise = the pure signal SPL alone.
Signal only
—
Formula
Combine: L_total = 10·log₁₀(Σᵢ 10^(Lᵢ / 10)) Subtract background: L_signal = 10·log₁₀(10^(L_total / 10) − 10^(L_bg / 10)) N equal sources: L_N = L₁ + 10·log₁₀(N)
- · Golden rule: two equal incoherent sources add to +3.01 dB (10·log₁₀(2)). So 80 + 80 = 83 dB, 90 + 90 = 93 dB, and so on.
- · Doubling rule: N equal sources → +10·log₁₀(N) dB. Four sources = +6 dB; ten sources = +10 dB; one hundred sources = +20 dB.
- · 10 dB dominance rule: if one source is more than 10 dB above the rest, the others together usually shift the total by less than 0.5 dB — to lower the total, attack the loudest source first.
- · The background-subtraction formula only applies to a measured total (the source-of-interest plus the background). If background ≥ total, the math gives log(0 or negative), meaning the signal is buried in the noise floor.
- · The combination formula assumes incoherent sources — true for everyday noise. Coherent sources at the same frequency and phase can add to +6 dB through constructive interference, but that only matters for engineered or simulated signals.
- · Reference: ISO 9613, ANSI/ASA S1.1, and any standard acoustics text (e.g. Beranek, "Noise and Vibration Control").
Frequently asked
Why do 80 dB and 80 dB not add up to 160 dB?
The decibel is a logarithmic scale of power (or pressure squared) ratios, not a linear quantity. Adding two equal-power sources doubles the total power, and a doubling on the log scale is +10·log₁₀(2) ≈ +3.01 dB. So 80 + 80 dB is not 160 dB; it is 83 dB. To gain another 3 dB you need to double again — i.e. four 80 dB sources combined sit at 86 dB. The 160 dB answer comes from applying linear intuition (80 + 80 = 160) to what is fundamentally a logarithm.
How do I subtract background noise from a measurement?
Measure the total L_total with the source running, then turn the source off and measure the background L_bg. Pure signal = 10·log₁₀(10^(L_total/10) − 10^(L_bg/10)). For example, a machine running reads 75 dB and the same room with it off reads 70 dB → the machine alone = 10·log₁₀(10^7.5 − 10^7) ≈ 73.3 dB. Caveat: if L_total − L_bg < 3 dB the correction has large uncertainty (the background is too close to the total for the measurement itself to be reliable); ISO 11200 recommends at least a 6 dB gap before subtracting, with 10+ dB ideal.
I have heard "+3 dB doubles the sound" and "+10 dB sounds twice as loud" — which is right?
Both are correct, but they refer to different things. +3 dB doubles the *sound power* (pressure-squared) — the physical quantity this tool computes. +10 dB doubles the *perceived loudness* (sones) — the psychoacoustic quantity, derived from Stevens' power law (loudness ∝ I^0.3). So two 80 dB sources have twice the energy (+3 dB → 83 dB) but barely sound louder; you need 90 dB before it sounds twice as loud as 80 dB.
Related tools
Ohm's Law Calculator (V / I / R / P)
Enter any two of voltage, current, resistance, or power — the calculator solves for the other two using V = IR and P = VI.
Speed, Distance & Time Calculator
Enter any two of distance, time and speed to get the third — with km/h, mph, m/s, km, miles, hours and minutes supported.
Density Calculator (mass / volume)
Compute density from mass and volume (ρ = m / V), or solve for the missing variable. Built-in reference table for 19 common substances.
Projectile Motion Calculator
Enter launch speed, angle and height to compute projectile range, peak height and flight time (no air resistance). Pick from Earth, Moon, Mars and more.
Wind Chill Calculator
Compute the wind chill (feels-like temperature) from air temperature and wind speed using the 2001 Environment Canada / US NWS formula, with frostbite risk levels.
Dew Point Calculator
Compute dew point from air temperature and relative humidity using the Magnus formula — handy for HVAC, photography and weather analysis.
Kinetic Energy Calculator (KE = ½ m v²)
Compute kinetic energy KE = ½ m v² with mixed units (kg / g / lb and m/s / km/h / mph) and see the result in joules, kilojoules, food calories, foot-pounds and watt-hours.
Half-Life & Exponential Decay Calculator
Enter any three of initial amount, remaining amount, elapsed time and half-life to solve for the fourth — useful for radioactive decay, drug pharmacokinetics and radiometric dating.
Resistor Color Code Calculator (4 / 5 band)
Pick the colour bands and instantly read the resistance and tolerance — 4-band and 5-band notations supported, with Ω / kΩ / MΩ formatting and a closest E12 / E24 preferred-value check.
GPS Distance Calculator (Haversine)
Enter two latitude/longitude pairs to compute the great-circle distance using the haversine formula (km, miles, nautical miles), with bearing and midpoint.
Solution Dilution Calculator (C₁V₁ = C₂V₂)
Solve any one of C₁, V₁, C₂, V₂ from the dilution equation C₁V₁ = C₂V₂ — a daily lab essential for chemistry, biology and pharmacy work.
Resistor Parallel / Series Calculator
Enter up to 8 resistor values to see the series total (R₁ + R₂ + …) and the parallel total (1 / Σ(1/Rᵢ)) at the same time.
Wavelength ↔ Frequency Calculator
Convert between electromagnetic wavelength and frequency via c = λf, with the matching spectrum band (radio / microwave / visible / X-ray / γ) and photon energy.
Tank Volume Calculator
Compute the capacity of vertical or horizontal cylindrical, rectangular and spherical tanks, including partial-fill volumes at a given liquid level.
Pendulum Period Calculator (T = 2π√L/g)
Enter the pendulum length and local gravity to get the period, frequency and angular frequency, with Earth/Moon/Mars/Jupiter presets — and reverse-solve for the length needed to hit a target period.
Heat Index Calculator
Enter air temperature and relative humidity to get the apparent temperature (NOAA Rothfusz heat index) and the corresponding heat-stress risk band.
Vehicle Stopping Distance Calculator
Enter speed, reaction time and road friction to estimate reaction, braking and total stopping distance.
Snell's Law Refraction Calculator
Enter the refractive indices of two media and an angle of incidence — get the refraction angle and critical angle from Snell's law (n₁ sin θ₁ = n₂ sin θ₂).
Capacitor Energy Calculator
Enter capacitance (F, mF, µF, nF, pF) and voltage to compute the stored energy (E = ½CV²) and charge (Q = CV) on a capacitor.
Boiling Point at Altitude Calculator
Enter altitude to compute the boiling point of water (°C / °F) and local air pressure using the ICAO standard atmosphere and the Antoine equation — useful for hiking, cooking and high-altitude baking.
Specific Heat (Q = mcΔT) Calculator
Solve Q = m × c × ΔT for any one of heat energy, mass, specific heat capacity or temperature change — with presets for water, aluminium, iron, copper, glass, air and more.
pH and Hydrogen Ion Concentration Calculator
Convert between pH, pOH, hydrogen-ion concentration [H⁺] and hydroxide concentration [OH⁻] — with acid / neutral / alkaline classification.
Ideal Gas Law (PV = nRT) Calculator
Pick the unknown (P, V, n or T), enter the other three and PV = nRT is solved instantly — works in Pa / kPa / atm / bar / mmHg / psi, m³ / L / mL, mol / mmol / kmol and K / °C / °F.