Passive Radiator Added Mass Calculator
Enter the enclosure, passive-radiator, and active-driver data to estimate the weight each radiator needs for the target tuning. The result also checks whether the chosen radiators have enough displacement and whether an entered added-mass limit is exceeded.
Added mass per radiator69.72
- Final moving mass per radiator
- 169.72
- Factory-mass box tuning
- 39.08
- Total active-driver displacement
- 200
- Total radiator displacement
- 495
- Radiator-to-driver displacement ratio
- 2.48
- Minimum radiator count
- 1
- Design status
- Add 69.7 g to each radiator; radiator displacement meets the 2:1 minimum with 1 radiator.
Mass values are per passive radiator, with all radiators treated as identical.
The displacement check uses the common minimum target of twice the active-driver one-way displacement.
How to use this calculator
- Enter the finished net enclosure volume after subtracting all internal displacements.
- Enter the target tuning frequency and the number of identical passive radiators in the box.
- Copy the passive radiator Fs, moving mass, Sd, Xmax, and any published added-mass limit from its datasheet.
- Enter the active-driver count, Sd, and one-way Xmax to check radiator displacement against driver displacement.
How the added mass is calculated
A passive radiator is treated as a mass on a suspension, coupled to the spring of the air in the enclosure. Adding weight raises the moving mass, which lowers the installed resonance. This calculator works backward from the desired box tuning and returns the final moving mass and the bolt-on mass for each radiator.
Inputs are converted before the calculation: enclosure volume from liters to cubic meters, moving mass from grams to kilograms, cone area from cm² to m², and excursion from millimeters to meters. With Vb as box volume, Fb as target tuning, Fp as the radiator free-air resonance, Np as radiator count, M0 as factory moving mass, and Sp as radiator Sd, the radiator compliance is:
Cms = 1 / ((2 pi Fp)^2 x M0)
The compliance is converted to the radiator equivalent volume:
Vas,p = rho x c^2 x Cms x Sp^2
The calculator uses rho = 1.204 kg/m^3 and c = 343 m/s. Multiple identical radiators share the same box, so the installed compliance per radiator is:
Cms,r = Cms / (1 + Np x Vas,p / Vb)
The required final moving mass per radiator is then:
Mtarget = 1 / ((2 pi Fb)^2 x Cms,r)
The headline result is Madd = Mtarget - M0. A negative value means the target tuning is above the factory-mass installed resonance. In that case, adding weight cannot reach the target; the design would need a lighter radiator, a different box volume, a different radiator count, or a lower target tuning.
What moves the result most
Lower target tuning, smaller box volume, larger radiator Sd, and more radiators all increase the mass required for each radiator. The calculator does not divide a one-radiator mass by the number of radiators. It recomputes the installed compliance seen by each radiator after the radiator count changes.
The displacement check compares total active-driver swept volume with total passive-radiator swept volume. Active displacement is Nd x Sd x Xd; passive-radiator displacement is Np x Sp x Xp. The status flags designs below a 2:1 radiator-to-driver displacement ratio, a common minimum recommendation for passive-radiator systems.
What this leaves out
This is a small-signal lumped-parameter estimate. It does not model full frequency response, F3, amplifier power, excursion at every frequency, air leaks, box losses, suspension nonlinearity, orientation sag, or aging. Use the result to choose starting weights, then measure the finished enclosure and adjust the mass experimentally.
Worked example
Suppose a 30 L enclosure is tuned to 30 Hz with one passive radiator. The radiator has Fp = 15 Hz, M0 = 100 g, Sd = 330 cm², and Xmax = 15 mm. The active driver has Sd = 200 cm² and Xmax = 10 mm.
The free-air compliance is about 0.001126 m/N, and the radiator equivalent compliance volume is about 0.1737 m^3. In the 30 L box, the installed compliance is about 0.0001658 m/N. Solving for a 30 Hz tuning gives a final moving mass of about 169.7 g, so the added-mass result is 69.7 g. The factory-mass box tuning is about 39.1 Hz, so this target can be reached by adding weight.
The active driver displaces 200 cm³, while the passive radiator displaces 495 cm³. The ratio is 2.48:1, so one radiator clears the 2:1 displacement check.
Common questions
How much weight should I add to a passive radiator?
Use the added mass per radiator result as the starting bolt-on weight for each identical passive radiator. If the result is positive, add that much mass to each radiator before measuring the finished enclosure. If the result is negative, the target tuning is too high for added mass to solve.
Why does adding mass lower passive-radiator tuning?
A passive radiator behaves like a moving mass on a spring. The enclosure air and the radiator suspension provide the spring, and the cone, surround, spider, and weights provide the mass. Increasing the mass lowers the resonant frequency in the same way a heavier oscillator moves more slowly.
Do two passive radiators need the same added mass?
Yes, when they are identical radiators in the same enclosure, each should receive the same added mass. The calculator reports mass per radiator after accounting for the number of radiators. Do not calculate one radiator and split that mass between two radiators.
How large should a passive radiator be compared with the woofer?
A common minimum is for total passive-radiator displacement to be at least twice the active drivers one-way displacement. The calculator reports the displacement ratio and the minimum number of the entered radiators needed to meet that 2:1 target. More margin may be needed for high-power subwoofers.
What does a negative added-mass result mean?
It means the target tuning is above the predicted factory-mass box tuning. Added weight only lowers tuning, so the entered parts cannot reach that target by adding mass. Try a lower target tuning, a different box volume, fewer or smaller radiators, or a passive radiator with less factory moving mass.
How can I verify the final tuning frequency?
Measure the finished enclosure impedance and find the minimum between the two low-frequency impedance peaks. That minimum is the passive-radiator system tuning. Add or remove small amounts of mass and remeasure until the minimum lands at the desired frequency.