NC Curve Calculation from Octave-Band Measurements — Step-by-Step

Noise criteria ratings — NC, NR, RC — all require the same fundamental operation: compare octave-band sound pressure levels to a set of reference curves and find the highest curve that any measurement band touches or exceeds. This sounds simple, but it is easy to make errors in practice, particularly in identifying the controlling band and handling the 63 Hz octave (which NC omits but RC includes). This article calculates NC and RC Mark II ratings from the same set of measurements.

The Measurements

Background noise measurements in an open-plan office, HVAC system running at design airflow. Measured using a calibrated class 1 sound level meter in octave-band mode, averaged over 5 minutes with occupants absent.

Measured octave-band SPL (dB re 20 μPa):

The 63 Hz band is notably elevated — this is common with variable-air-volume (VAV) box systems and large ductwork.

Part 1 — NC Rating Calculation

The NC rating system uses octave bands from 63 Hz to 8000 Hz (though some references use 125–8000 Hz — check whether your source includes the 63 Hz octave). The standard NC contours were tabulated by Beranek (1957) and are reproduced in ASHRAE.

NC Contour Reference Values (dB SPL)

Tangent Curve Method

For each octave band, subtract the measured level from the NC contour value at that frequency. The lowest difference (closest to zero, or the smallest excess of NC over measured) identifies the controlling band.

Comparing measured values against NC-30:

The measured spectrum exceeds NC-30 at all bands. Let's check NC-35:

Comparing measured values against NC-35:

Still exceeds at all bands. Check NC-40:

Comparing measured values against NC-40:

The measured spectrum falls below NC-40 at all octave bands. The NC rating is the highest curve that any band just touches — which was NC-35 (exceeded at 500 and 1000 Hz by 1.5 dB each).

The 125 Hz band had the largest excess over NC-35 (4.5 dB). If that single band were the ruling criterion, the NC rating would be... check NC-40 at 125 Hz: measured 56.5 dB vs NC-40 = 57.0 dB, margin +0.5 dB — so the spectrum fits within NC-40.

NC Rating = 40 — the spectrum just fits within NC-40, with the 125 Hz band as the controlling band (margin +0.5 dB from NC-40).

To report this more precisely: since the spectrum exceeds NC-35 at six of eight bands and the closest fit to any NC contour is NC-40 at 125 Hz, the measured background noise is NC-40.

Part 2 — Controlling Frequency Band

To identify which band drives the rating, compute how many dB each band exceeds the NC-40 contour:

The 125 Hz band is the controlling frequency — it is the band closest to the NC-40 contour, with only 0.5 dB of margin. Any noise source that adds approximately 3–4 dB to the 125 Hz band (within logarithmic summation) would push the rating to NC-45.

Part 3 — RC Mark II Calculation

The RC Mark II method (ASHRAE 2011, from Blazier 1997) evaluates not just the level but the spectral balance of HVAC noise. It identifies whether the noise sounds like rumble, balanced, or hiss, and whether it contains audible tonal components.

Step 1 — Calculate RC Level

The RC level is the arithmetic average of octave-band SPL at 500, 1000, and 2000 Hz:

RC = (L_500 + L_1000 + L_2000) / 3 = (41.5 + 35.5 + 30.5) / 3 = 107.5 / 3 = 35.8 → RC-36

Step 2 — Determine Spectral Quality (R, N, or H)

RC Mark II defines a reference spectrum through the RC level and evaluates whether low-frequency bands are elevated (rumble) or high-frequency bands are elevated (hiss).

R-curve (Rumble) reference values (bands elevated more than reference = rumble character):

• 16 Hz: RC + 35 dB
• 31.5 Hz: RC + 29 dB
• 63 Hz: RC + 22 dB
• 125 Hz: RC + 17 dB

• 2000 Hz: RC + 0 dB
• 4000 Hz: RC − 5 dB
• 8000 Hz: RC − 10 dB

Low-frequency quality check:

Both 63 Hz and 125 Hz exceed their R-curve thresholds. When any low-frequency band exceeds its threshold by more than 5 dB (in intensity units — LI terms), the noise is classified as "R" (Rumble character).

The excess in intensity units: at 63 Hz, +5.0 dB = 10^(5.0/10) − 1 = 2.16 (215% excess). At 125 Hz, +3.5 dB = 10^(3.5/10) − 1 = 1.24 (124% excess).

High-frequency quality check:

No hiss issues.

RC Mark II Rating: RC-36(R) — the noise is at RC-36 level with a rumble character, meaning low-frequency content is perceptually prominent.

Step 3 — Interpret the RC Mark II Rating

The "(R)" designation means occupants will likely perceive the noise as having a booming or rumbling quality, even though the 500–2000 Hz levels are within acceptable limits. This often manifests as a perception that the HVAC system is "heavy" or "powerful" even when speech interference is not an issue.

The cause in this case is the 63 Hz band at 63.0 dB — characteristic of large VAV air handler units and main duct sections with high air velocity. Corrective measures include:

1. Duct lining with 25–50 mm mineral wool for 1–2 m downstream of the air handler
2. Duct silencers (splitter attenuators) at the VAV box
3. Flexible duct connections to break structure-borne transmission
4. Reduce duct velocity below 5 m/s in the final 10 m of ductwork

NC vs RC Mark II Summary

The NC rating suggests the space is on the upper acceptable limit but functional. The RC Mark II rating reveals a quality problem that NC misses — the low-frequency emphasis will be perceptible as a rumble even though no single NC contour is exceeded by more than 0.5 dB.

Practical Workflow Summary

1. Measure octave-band SPL from 63 (or 31.5) to 8000 Hz with the HVAC at design flow
2. Compare measured values to NC contours at each band — find the highest contour that any band just touches
3. Identify the controlling band (smallest margin to the NC contour)
4. Calculate RC level: average of 500, 1000, 2000 Hz bands
5. Check R and H curve thresholds to identify spectral quality
6. Report both ratings: e.g., NC-40 / RC-36(R)