Physics · 5 min read
How to Convert Between Tuned RPM and Velocity Stack Length
N = (C × 60 × S) / (4 × Ls × O) — the same identity, flipped
If the tract is already on the engine, the useful question is which RPM that length is a quarter-wave of. This tutorial rearranges Ls = (C × 60 × S) / (4 × N × O) to solve for N, works a 400 mm four-stroke example, and points at the Velocity Stack Calculator’s length and RPM modes. Neither direction is a dyno.
Written by the My Calculator Stack editorial team. About our methods
Length and RPM are two reads of one quarter-wave identity. Cam timing still moves the real peak. Solving for RPM does not measure horsepower.
1.When you already have a length
Builders often measure a runner-plus-stack that already exists, or they are stuck with a trumpet that fits the hood. Then you do not want a new Ls — you want the engine speed that matches the length you have, at a chosen odd order. The reverse is the usual design path: pick RPM and O, then cut length. Both are the same equation. Mixing them up (using a stack-only measurement as Ls, or a redline as if it were peak torque) is how the number disagrees with another website.
2.The pair of solves
Forward: Ls = (C × 60 × S) / (4 × N × O). Reverse: N = (C × 60 × S) / (4 × Ls × O). A third rearrange, C = (Ls × 4 × N × O) / (60 × S), is a consistency check, not a thermometer. Length Ls here is the effective tract in meters. If you measured 400 mm, use 0.400 m. S and O stay in both directions. The Velocity Stack Calculator exposes all three as solve modes so you do not rearrange on paper.
\[ N=\frac{C\times 60\times S}{4 L_s O} \]
3.Worked example: 400 mm on a four-stroke
Take C = 343 m/s, S = 2, O = 3, and Ls = 0.400 m. Then N = (343 × 60 × 2) / (4 × 0.400 × 3) = 41160 / 4.8 = 8575 rpm. The same length at O = 1 would be a 25725 rpm “tune,” which is not a street target — it is a reminder that order and length trade. At the calculator defaults, 0.5717 m and O = 3 return 6000 rpm, which is the forward golden run backwards. Two-stroke S = 1 at 400 mm and O = 3 is half the RPM (4287.5 rpm) because S sits in the numerator.
\[ N=\frac{343\times 60\times 2}{4\times 0.400\times 3}=8575\,\mathrm{rpm} \]
4.What not to convert
Do not convert a trumpet-only measurement and then compare it to a valve-to-mouth Ls from another chart. Do not treat the RPM result as peak-power RPM; it is the quarter-wave speed for that length and order. End correction and an existing runner change the stack remainder, not the N ↔ Ls identity for the effective length. If the hood forces 400 mm, read 8575 rpm at O = 3 as “this tube is a high-RPM third harmonic,” then decide whether that is the band you drive in.
5.Switch solve mode instead of the algebra
On the Velocity Stack Calculator, choose Length when you have a target RPM, or Engine speed when you have a measured tract. Stroke and order stay visible. Temperature still sets C unless you override it. The odd-harmonic table in RPM mode lists the engine speed each order would want at that same length — useful when 400 mm is O = 3 at 8575 rpm and you want to see O = 5 on the same tube. Then confirm on a dyno; the rearrange is not a pull.
Try it yourself
Open the related calculator and put these formulas to work.