Belt Tension Calculator
Belt power is (T₁ − T₂)v with T₁/T₂ = e^(μθ): a flat belt limited to 2000 N at 20 m/s with μ = 0.3 over 165° transmits 20.826 kW.
20.8260376041142 kW
Full answer, then cut to fewer decimals (not rounded):
- 20.8260376041142 kW
- 20.826037604114 kW
- 20.82603760411 kW
- 20.8260376041 kW
- 20.826037604 kW
- 20.82603760 kW
- 20.8260376 kW
- 20.826037 kW
- 20.82603 kW
- 20.8260 kW
- 20.826 kW
- 20.82 kW
- 20.8 kW
- Centrifugal tension Tc = mv²
- 200 N
- Tight-side tension T₁ = Tmax − Tc
- 1800 N
- Slack-side tension T₂
- 758.698 N
- Tension ratio T₁/T₂ = e^(μθ)
- 2.37249
- Speed for maximum power v = √(Tmax/3m)
- 36.5148 m/s
Step-by-step solution
- T₁/T₂ = e^(μθ) = e^(0.3 × 2.88) = 2.37249
- T₁ = 2000 − 200 = 1800 N, T₂ = 758.698 N
- P = (T₁ − T₂) v = 1041.3 × 20 = 20826 W
Belt Tension Formula
T₁/T₂ = e^(μθ), P = (T₁ − T₂) v
μ friction (μ/sin β for a V-belt), θ wrap angle, Tc = mv²
Worked Example
A flat belt, Tmax = 2000 N, 0.5 kg/m, 20 m/s, μ = 0.3, θ = 165°:
- T₁/T₂ = e^(μθ) = e^(0.3 × 2.88) = 2.37249
- T₁ = 2000 − 200 = 1800 N, T₂ = 758.698 N
- P = (T₁ − T₂) v = 1041.3 × 20 = 20826 W
Tight-side tension T₁ = Tmax − Tc: 1800 N · Slack-side tension T₂: 758.698 N · Tension ratio T₁/T₂ = e^(μθ): 2.37249 · Speed for maximum power v = √(Tmax/3m): 36.5148 m/s
More Theory of Machines and Vibrations Calculators
-
Gear Train Calculator
N₁/Nout = Π driven teeth ÷ Π driving teeth
train value = 1/speed ratio
Example: A compound train 20/60 then 15/45 driven at 1200 rpm: Output speed N = 133.333 rpm.
-
Natural Frequency Calculator
ωn = √(k/m), fn = ωn/2π, ζ = c/2√(km)
m mass, k stiffness, c damping coefficient
Example: A 10 kg mass on a 4000 N/m spring: Natural frequency fn = 3.1831 Hz.
-
Transmissibility Calculator
TR = √[1 + (2ζr)²] ÷ √[(1 − r²)² + (2ζr)²]
r = ω/ωn frequency ratio, ζ damping ratio
Example: A machine running at twice the natural frequency with ζ = 0.1: Transmissibility TR = 0.355862.
-
Flywheel Calculator
ΔE = I ω² Cs = m k² ω² Cs
Cs = (ωmax − ωmin)/ω, k radius of gyration
Example: ΔE = 5000 J at 600 rpm with Cs = 2 % and k = 0.5 m: Moment of inertia I = 63.3257 kg·m².
Frequently asked questions
At what speed does a belt transmit maximum power?
When centrifugal tension is one third of the maximum tension: v = √(Tmax/3m).
Why does a V-belt grip better than a flat belt?
The wedge action raises the effective friction coefficient to μ/sin β, where 2β is the groove angle.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Belt Tension Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/belt-tension-calculator/
IEEE
Scientific Converters, "Belt Tension Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/belt-tension-calculator/