Passive radiators are a good substitute for vents because they can be mass-loaded to tune for frequency and because they eliminate the possibility of vent wind noise. The inside total volume is the same as if you were tuning with a vent. Vent length versus inside cabinet dimensions is no longer an issue, and outside cabinet dimensions have to accommodate the speaker in the front and the passive radiator also in the front or on one of the sides. Passive radiators should always be two to four inches larger in diameter than the woofer. Take the passive radiator cone volume into account.
Plug the Thiele-Small parameters of your woofer into a ported (or vented) enclosure calculator. Woofers with a Qts of .4 or lower are suitable for vented or passive radiator designs.
Use the inside cabinet volume derived with the speaker volume calculator to design a cabinet suitable for vent tuning, which also physically accommodates a passive radiator or multiple radiators with roughly twice the moving area of the woofer.
Use an Internet port size calculator to find the inside cross-section area and length of the right vent for your speaker/cabinet.
Multiply the vent area and length to get the air volume in cubic inches. Divide that figure by 47 to get the air column's mass in grams. Your passive radiator's published moving-mass specification should centre around the same mass as the column of air in your calculated vent size would weigh.
Tune the passive radiator to a lower frequency by using a threaded rod or bolt to add mass. This will make the system behave like a sealed system above the initial tuning frequency, but a vented system below that frequency, making the bass tighter and deeper. Tuning hardware is usually supplied with commercially available passive radiators.
At sea level, air weighs 29 grams for every .79 cubic feet of air, or 1 gram for every 47 cubic inches.