Passive Radiator Calculator

Optimize your speaker enclosure’s low-frequency performance. Use our passive radiator calculator to determine the ideal tuning frequency (Fb) and required mass for your subwoofer or speaker design.

Mass Addition Reference Table

Added Mass (g)	Total Mass (g)	New Fs (Hz)	System Fb (Hz)

Table calculated using the provided box volume and PR specs.

What is a Passive Radiator Calculator?

A passive radiator calculator is a specialized acoustic design tool used by audio engineers and DIY speaker builders to predict the resonant behavior of a “drone cone” system. Unlike a standard ported enclosure that uses a hollow tube to tune the air inside the box, a passive radiator system uses a non-powered driver diaphragm. This tool helps you find the exact point where the enclosure’s internal air compliance and the radiator’s mass interact to create a bass boost.

Using a passive radiator calculator is essential because, unlike ports, passive radiators have their own physical compliance (suspension) and mass. If you don’t calculate these variables correctly, your speaker might suffer from poor transient response, excessive cone excursion, or a complete lack of low-end reinforcement. This calculator specifically helps you determine how much “added mass” is needed to reach a specific target frequency, such as 20Hz or 30Hz.

Common misconceptions include the idea that a passive radiator is just a “fake speaker.” In reality, it functions identically to the slug of air in a port, but with the added benefits of no port noise (chuffing) and the ability to fit into smaller cabinets where a long port simply wouldn’t fit.

Passive Radiator Calculator Formula and Mathematical Explanation

The physics of a passive radiator enclosure is based on a fourth-order high-pass filter alignment. The primary goal of the passive radiator calculator is to solve for the system tuning frequency ($F_b$).

The Core Formulas

1. Effective Free Air Resonance: When you add mass to a radiator, its natural resonance drops.
   
   Fs_adj = Fs * sqrt( Mms / (Mms + Madd) )
2. System Tuning Frequency: The final tuning frequency ($F_b$) is a result of the relationship between the box volume and the radiator’s compliance.
   
   Fb = Fs_adj * sqrt( (Vas / Vb) + 1 )

Variable	Meaning	Unit	Typical Range
Vb	Net Box Volume	Liters (L)	5L – 200L
Vas	Compliance Equivalent Volume	Liters (L)	10L – 500L
Fs	Free Air Resonance	Hertz (Hz)	15Hz – 45Hz
Mms	Moving Mass	Grams (g)	50g – 1000g
Madd	Added Weight	Grams (g)	0g – 500g

Practical Examples (Real-World Use Cases)

Example 1: High-Output 12-inch Subwoofer

Imagine you have a 40-liter enclosure and a 12-inch passive radiator with a $V_{as}$ of 80L and an $F_s$ of 20Hz. The radiator has a base mass ($M_{ms}$) of 200g. Using the passive radiator calculator, you see the native tuning is about 34.6 Hz. If your goal is a deep-reaching home theater sub tuned to 20Hz, the calculator will show you need to add approximately 400g of mass to the radiator’s carrier.

Example 2: Compact Desktop Monitor

A small 5-liter box uses a 5-inch passive radiator ($V_{as}$: 6L, $F_s$: 45Hz, $M_{ms}$: 15g). The passive radiator calculator determines the natural tuning is 66 Hz. This is perfect for a small speaker to provide punchy upper-bass without the turbulence of a tiny, narrow port.

How to Use This Passive Radiator Calculator

1. Measure your Enclosure: Calculate the internal volume (Vb). Subtract the volume taken up by the woofer motor and internal bracing.
2. Input PR Specs: Enter the $V_{as}$, $F_s$, and $M_{ms}$ from the manufacturer’s spec sheet. These are critical for an accurate passive radiator calculator result.
3. Adjust Mass: If the calculated $F_b$ is too high, increase the “Added Mass” value. If it is too low, you may need a different radiator or a larger box.
4. Analyze the Chart: Look at the Tuning Shift Curve to see how sensitive your tuning is to small mass changes.
5. Build and Verify: Use the “Copy Results” feature to save your data before starting your physical build.

Key Factors That Affect Passive Radiator Results

• Radiator Surface Area (Sd): It is generally recommended that the passive radiator have 1.5x to 2x the surface area of the active driver to avoid “over-driving” the radiator suspension.
• Enclosure Stiffness: A passive radiator calculator assumes a perfectly rigid box. If the walls flex, the tuning frequency will shift and efficiency will drop.
• Mass Selection: Adding too much mass can lead to “droop” or “sag” in the suspension over time, especially if the radiator is mounted horizontally (facing up or down).
• Air Leaks: Unlike a ported box, a PR box must be 100% airtight. Even a tiny leak around the terminal cup will ruin the pressure relationship.
• Vb to Vas Ratio: This “Alpha” value determines the shape of the roll-off. A high alpha usually results in a peaky response, while a lower alpha is smoother.
• Ambient Temperature: Cold temperatures stiffen the PR surround, temporarily raising the $F_s$ and $F_b$ until the material warms up.

Frequently Asked Questions (FAQ)

1. Why use a passive radiator instead of a port?

Passive radiators allow for low tuning in very small boxes where a physical port would be too long to fit. They also eliminate air turbulence noise.

2. Can I use a regular speaker as a passive radiator?

Yes, by leaving the terminals disconnected or shorted. However, dedicated PRs are better as they allow for easy mass addition and have more excursion capability.

3. How do I add mass to a passive radiator?

Most PRs have a threaded bolt on the back. You can use large washers, lead weights, or specialized discs. Always use the passive radiator calculator to check your math first.

4. What is ‘Radiator Slop’?

This occurs when the radiator suspension is too soft for the added mass, causing it to wobble or sag. High-quality PRs have stiffer suspensions to handle heavy loads.

5. Does the orientation of the radiator matter?

Yes. If mounted on the bottom, gravity pulls the mass down, reducing the available excursion in one direction. Side-mounting is usually preferred.

6. How many radiators should I use?

Usually, two radiators of the same size as the driver, or one radiator that is one size larger than the driver (e.g., a 12″ PR for a 10″ driver).

7. Will a passive radiator calculator work for multiple PRs?

Yes, but you must treat them as one. Double the $V_{as}$ and $M_{ms}$ values if they are identical and used in the same chamber.

8. How accurate is the tuning prediction?

Typically within 5-10%. Physical testing with a woofer tester (like DATS) is recommended for final fine-tuning of the added mass.