Inputs
Example data
| Spoke length (mm) | Frequency (Hz) | Diameter (mm) | Material | Tension (kgf) | Tension (N) |
|---|---|---|---|---|---|
| 292 | 350 | 2.00 | Stainless steel | 105.07 | 1030.65 |
| 292 | 310 | 2.00 | Stainless steel | 82.42 | 808.29 |
| 284 | 305 | 2.00 | Carbon steel | 75.47 | 740.14 |
| 286 | 360 | 2.00 | Aluminum | 36.68 | 359.68 |
| 290 | 340 | 1.60 | Titanium | 35.88 | 351.85 |
| 275 | 315 | 2.00 | Brass | 81.73 | 801.52 |
| 260 | 330 | 1.80 | Stainless steel | 59.98 | 588.22 |
| 300 | 320 | 2.34 | Stainless steel | 126.90 | 1244.50 |
These examples use the frequency method with a round spoke model.
Formula used
A spoke can be approximated as a vibrating string. If the spoke length is L,
the vibration frequency is f, and the linear mass density is μ,
then the tension is:
T = 4 · L² · f² · μ
Lin meters,fin hertz,μin kg/m, givingTin newtons.- When diameter and density are used:
μ = ρ · A, whereA = π(d/2)². - Spoke stress is estimated as
σ = T / A. - Elastic elongation is estimated as
ΔL = (T · L) / (A · E).
Real wheels include damping, bend stiffness, and boundary effects. Treat results as an engineering estimate, then confirm with a calibrated tensiometer and rim limits.
How to use this calculator
- Measure your spoke length in millimeters, or use your build sheet.
- Pluck the spoke and record its dominant frequency in hertz.
- Select the spoke diameter, or enter a custom mid-section diameter.
- Pick the spoke material, or enter a custom density.
- Optionally enter spoke mass or linear density for higher accuracy.
- Click calculate, then review tension, stress, and elongation.
- Export your results to CSV or PDF for workshop notes.
Tip: If you compare multiple spokes, keep the same length reference and pluck position each time.
Spoke tension in plain numbers
Spoke tension is the pulling force along a spoke that compresses the rim and stabilizes the wheel. It is commonly shown in newtons or kilogram‑force. Use 1 kgf ≈ 9.80665 N for quick checks. Even tension matters more than extreme tension.
Typical ranges you can compare
Many road wheels run about 900–1200 N per drive‑side rear spoke, with non‑drive side lower due to dish. Mountain wheels are often 700–1100 N, depending on rim strength and lacing. Follow the rim maker’s maximum; many carbon rims specify 1000–1300 N. For disc fronts, 900–1100 N is common on strong rims.
Frequency method used here
The vibrating‑string method is T = 4·L²·f²·μ. Example: L = 0.292 m, f = 350 Hz, μ = 0.000885 kg/m gives T ≈ 1051 N. A higher pluck frequency usually means higher tension when length and μ are unchanged.
Material density and diameter effects
Linear mass density μ depends on material and diameter: μ = ρ·A with A = π(d/2)². Stainless steel is roughly 7850 kg/m³, aluminum about 2700, titanium about 4500, and brass about 8500. A 2.0 mm spoke has 56% more area than a 1.6 mm spoke, raising μ and lowering pitch at the same tension.
Stress from your result
Spoke stress estimates help sanity‑check results: σ = T/A. For a 2.0 mm spoke, A ≈ 3.14×10⁻⁶ m². If T = 1100 N, then σ ≈ 350 MPa. Stress concentrates near the elbow and threads, so consistency and rim limits matter.
Elongation you can feel
Elastic stretch is approximated by ΔL = (T·L)/(A·E). With steel E ≈ 200 GPa, T = 1100 N, L = 0.292 m, and d = 2.0 mm, ΔL ≈ 0.51 mm. Titanium (E ≈ 110 GPa) stretches about 0.93 mm under the same inputs; aluminum (E ≈ 69 GPa) stretches more.
Workshop tips for better data
Pluck the same span each time and damp neighbors so harmonics do not confuse your tuner. Measure spoke length along the centerline, not the rim radius. Recheck after stress‑relieving; tension often drops slightly. If values look odd, enter measured spoke mass or μ for your exact model.
FAQs
1) Is the frequency method accurate enough for building wheels?
Yes for comparison and repeatability. Accuracy depends on correct spoke length and μ. Use the same pluck point, damp neighbors, and verify final builds with a calibrated tensiometer and the rim’s published tension limit.
2) What if I don’t know the spoke’s material density?
Pick a close material, then refine using measured spoke mass or linear density. Even a small μ error shifts tension noticeably, especially at high frequencies. If you have the spoke label, lookup its alloy and diameter.
3) Can I use measured spoke mass instead of diameter?
Yes. Weigh a known length of spoke, then compute μ = mass/length and enter it. This captures butting and coatings better than assuming a constant diameter, and improves the tension estimate for complex spoke profiles.
4) Why does my tensiometer reading differ from the calculator?
Tensiometers read deflection and need correct conversion for spoke type. Frequency readings depend on damping and where you pluck. Small errors in spoke length or μ can also shift results. Use both tools to spot outliers and confirm average tension.
5) What tension should I target for my wheel?
Target the rim manufacturer’s recommended range first. Rear drive‑side is usually the limiting side; the other side follows from dish. Aim for evenness within about ±10% across a side, then true the wheel without exceeding the maximum.
6) Does spoke length change the tension?
Length doesn’t directly change tension, but it changes pitch for a given tension. Longer spokes vibrate at lower frequency. That’s why accurate spoke length input matters when converting measured frequency into a tension value.