Belt Tension Calculator
Find the tight-side tension required in a belt drive to transmit a given power at a known belt speed. Use it when designing V-belt or flat-belt systems to size belts, pulleys, and shafts correctly.
About this calculator
Power transmission by a belt relies on the difference between tight-side tension T₁ and slack-side tension T₂. The effective tension (T₁ − T₂) equals transmitted force = Power / belt speed: T_eff = P(W) / v. The ratio of tensions is governed by the Euler–Eytelwein equation: T₁ / T₂ = e^(μθ), where μ is the coefficient of friction and θ is the wrap angle in radians. Combining these gives the tight-side tension: T₁ = T_eff × e^(μθ) / (e^(μθ) − 1). A larger wrap angle or higher friction coefficient reduces the required tight-side tension for the same power, which is why longer centre distances and tensioner pulleys are used in practice. This value determines shaft loads and minimum belt pre-tension.
How to use
Given: Power = 5 kW, belt speed = 10 m/s, wrap angle = 180°, friction coefficient μ = 0.3. Step 1 — effective tension: T_eff = 5,000 / 10 = 500 N. Step 2 — convert wrap angle to radians: 180 × π / 180 = 3.1416 rad. Step 3 — compute e^(μθ): e^(0.3 × 3.1416) = e^0.9425 ≈ 2.566. Step 4 — tight-side tension: T₁ = 500 × 2.566 / (2.566 − 1) = 500 × 2.566 / 1.566 ≈ 819 N. Enter your values to obtain T₁ directly.
Frequently asked questions
What is the difference between tight-side and slack-side belt tension?
Tight-side tension T₁ is the high tension on the pulling side of the belt as it leaves the drive pulley, while slack-side tension T₂ is the lower tension on the returning side. It is the difference T₁ − T₂, called effective tension, that actually transmits power. Both tensions must be considered when designing shafts and bearings, because the resultant shaft load depends on both. Insufficient pre-tension leads to belt slip, while excessive tension accelerates bearing and belt wear.
How does wrap angle affect belt drive performance and tension?
A larger wrap angle increases the maximum transmittable friction force between the belt and pulley, reducing the tight-side tension needed for the same power. This is described by the Euler–Eytelwein equation: T₁/T₂ = e^(μθ). A wrap angle below about 120° on the smaller pulley is generally considered marginal and often requires idler tensioners to compensate. Groove geometry in V-belts provides an effectively higher friction coefficient compared to flat belts, allowing more power per unit of tension.
Why does belt slip occur and how can I prevent it in my drive design?
Belt slip occurs when the demanded effective tension exceeds the maximum transmittable friction force, i.e., when the load torque drives T₁/T₂ beyond e^(μθ). It leads to power loss, heat generation, and rapid belt degradation. Prevention strategies include increasing wrap angle with an idler pulley, selecting a belt material with a higher friction coefficient, applying proper initial pre-tension, and ensuring the belt is not worn or contaminated with oil. Regular tension checks during maintenance are equally important.