SPL vs Power vs Distance

SPL from power:

SPL = Sensitivity + 10 × log₁₀(P)

Where Sensitivity is in dB/W/m (at 1 watt, 1 meter)

SPL vs distance (free field):

SPL_distance = SPL_reference − 20 × log₁₀(d / d_reference)

Equivalently: Every doubling of distance = −6 dB

Combined formula:

SPL = Sensitivity + 10 × log₁₀(P) − 20 × log₁₀(d)

Worked example:

Speaker sensitivity: 90 dB/W/m Power: 100W Distance: 1m

SPL = 90 + 10 × log₁₀(100) − 20 × log₁₀(1)
SPL = 90 + 20 − 0 = 110 dB

At 0.5m (half distance, in-car listening):

SPL = 90 + 20 − 20 × log₁₀(0.5) = 110 + 6 = 116 dB