dB Calculator
Calculate sound pressure level (SPL) and sound intensity level (SIL) in decibels from pascals or W/m². Free online physics dB calculator with distance attenuation.
About This Calculator
The dB Calculator computes sound pressure level (SPL) and sound intensity level (SIL) in decibels (dB) from physical sound measurements. Enter the sound wave pressure in pascals to get the SPL, or enter the sound intensity in watts per square meter to get the SIL. Optionally, enter the source power and distance to see how sound intensity attenuates with distance following the inverse square law.
The decibel is a logarithmic unit that expresses the ratio of a sound's pressure or intensity to a fixed reference. For SPL, the formula is SPL = 20 × log₁₀(P / P_ref) where P_ref = 20 µPa (0.00002 Pa), the threshold of human hearing. For SIL, the formula is SIL = 10 × log₁₀(I / I_ref) where I_ref = 10⁻¹² W/m². In free-field conditions, SPL and SIL are numerically equal.
This calculator is useful for audio engineers, acoustics researchers, physics students, sound designers, and anyone working with sound level measurements. Understanding dB levels is critical for hearing safety — prolonged exposure above 85 dB can cause hearing damage, and sounds above 120 dB can cause immediate pain.
Regional Notes
India: The Central Pollution Control Board (CPCB) sets ambient noise standards: 55 dB (day) / 45 dB (night) for residential areas, 65/55 dB for commercial zones, and 75/70 dB for industrial areas. Occupational exposure limits follow the Factories Act with 90 dB(A) for 8 hours.
United States: OSHA sets permissible noise exposure at 90 dB(A) for 8 hours with a 5 dB exchange rate. NIOSH recommends 85 dB(A) for 8 hours. The EPA identifies 70 dB as the safe 24-hour average to prevent hearing loss.
United Kingdom: The Control of Noise at Work Regulations 2005 set lower exposure action values at 80 dB(A) daily exposure, upper exposure action values at 85 dB(A), and exposure limit values at 87 dB(A) with hearing protection. HSE provides detailed guidance for workplace noise management.
Frequently Asked Questions
What is the formula for sound pressure level SPL?
The formula for SPL is SPL = 20 × log₁₀(P / P_ref) where P is the sound wave pressure in pascals and P_ref = 20 µPa (0.00002 Pa), the threshold of human hearing.
What is the formula for sound intensity level SIL?
The formula for SIL is SIL = 10 × log₁₀(I / I_ref) where I is the sound intensity in W/m² and I_ref = 10⁻¹² W/m², the reference intensity at the threshold of hearing.
How does sound intensity change with distance?
Sound intensity follows the inverse square law: I = P / (4πR²), where P is the source power in watts and R is the distance from the source in meters. Doubling the distance reduces intensity by a factor of 4 (about 6 dB).
What is the difference between SPL and SIL?
SPL (sound pressure level) is measured from sound wave pressure in pascals using 20×log, while SIL (sound intensity level) is measured from sound power per unit area in W/m² using 10×log. In a free field, SPL and SIL are numerically equal in dB.
How many dB is normal conversation?
Normal conversation typically measures 50-65 dB SPL at 1 meter distance. A whisper is about 20-30 dB, city traffic is 70-85 dB, a rock concert is 100-120 dB, and the threshold of pain is around 130 dB SPL.
Is the dB calculator free to use?
Yes, the dB calculator is completely free to use with no registration required. You can share results via URL.
What is the reference pressure used in SPL calculations?
The standard reference pressure for SPL calculations is 20 micropascals (0.00002 Pa), which corresponds to the threshold of human hearing at 1 kHz. This reference is used worldwide in acoustics and audio engineering.
How do you convert pascals to dB?
To convert pascals to dB SPL, use the formula: dB = 20 × log₁₀(P / 0.00002). For example, 1 Pa equals approximately 94 dB SPL, and 0.1 Pa equals approximately 74 dB SPL.