How to use this calculator
- Enter the power. Enter the power the belt transmits at the drive pulley.
- Enter the belt speed. Enter the belt (surface) speed — π · D · n for the drive pulley.
- Enter the wrap angle. Enter the angle of belt contact on the smaller pulley.
- Enter the friction coefficient. Enter the belt–pulley friction (use an effective μ for V-belts).
- Read the results. Read the effective, tight-side and slack-side tensions, and check the slack side stays positive.
How it works
The power a belt transmits is carried by the effective (net) tension — the difference between the two strands: Te = P / v with the power P in watts and the belt speed v in m/s, giving Te in newtons. This is the force the belt actually delivers at the pulley rim.
How that net force splits into a tight side T₁ and a slack side T₂ is set by
the capstan (Euler) belt-friction equation:
T₁ / T₂ = e^(μθ), where μ is the friction coefficient and θ is the
wrap (contact) angle in radians. It is the maximum tension ratio the
belt holds before slipping. Combining it with Te = T₁ − T₂ gives
T₁ = Te · e^(μθ)/(e^(μθ) − 1) and
T₂ = Te /(e^(μθ) − 1).
The slack-side tension T₂ must stay positive — if it falls to zero the belt
goes loose and slips. A larger wrap angle, a higher friction coefficient, or a
faster belt all raise the slip margin. V-belts grip far harder than flat belts
because the groove wedges the belt, multiplying the effective friction to
μ_eff = μ / sin(½ · groove angle). After sizing the strand
tensions, use the overhung load calculator
to estimate pulley shaft bearing reactions.
Worked example
Verified against the live calculator
A belt transmitting P = 5 kW at v = 10 m/s has an effective
tension Te = 5000 / 10 = 500 N. With a wrap angle θ = 180° (= π
rad) and friction μ = 0.3, the capstan ratio is
e^(0.3·π) = e^0.942 = 2.566. So the slack side is
T₂ = 500 / (2.566 − 1) ≈ 319 N and the tight side is
T₁ = 500 · 2.566 / 1.566 ≈ 819 N. Their difference,
819 − 319 = 500 N, equals Te — exactly the numbers the calculator returns.
Frequently asked questions
How do I calculate belt tension?
First find the effective (net) tension that carries the power: Te = P / v, with P in watts and v in m/s. Then split it across the two strands with the capstan equation T₁ / T₂ = e^(μθ): the tight side is T₁ = Te · e^(μθ)/(e^(μθ) − 1) and the slack side is T₂ = Te /(e^(μθ) − 1). Enter the power, belt speed, wrap angle and friction above and the calculator solves all three.
What is the difference between tight-side, slack-side and effective tension?
The tight side (T₁) is the strand pulling the load; the slack side (T₂) is the returning strand. Their difference is the effective (net) tension Te = T₁ − T₂, and that difference is what actually transmits the power: Te = P / v. The capstan equation fixes the ratio T₁/T₂ = e^(μθ), so once you know Te you know both strand tensions.
What is the capstan (Euler) equation?
The capstan or Euler belt-friction equation is T₁ / T₂ = e^(μθ), where μ is the friction coefficient and θ is the wrap (contact) angle in radians. It is the largest tension ratio the belt can hold before it slips — more wrap angle or more friction lets the tight side pull harder relative to the slack side, so the belt grips a bigger load.
Why must the slack-side tension stay positive?
The slack side still has to stay taut. If T₂ drops to zero the belt goes loose on the return run and slips on the pulley, losing drive. You raise the slack-side margin by increasing the wrap angle (an idler), the friction coefficient, or the belt speed — or by reducing the transmitted power.
How is V-belt tension different from a flat belt?
A V-belt sits in a groove, so the belt is wedged against both groove flanks. That multiplies the effective friction to μ_eff = μ / sin(½ · groove angle) — several times the flat value. Use that effective μ here and the same capstan equation applies; it is why a V-belt grips a much larger load than a flat belt of the same nominal friction.
Does it work in metric and imperial?
Yes — enter power in kW or hp and belt speed in m/s or ft/min; the tensions are shown in newtons or pound-force. Toggle SI/Imperial in the header.
Method & assumptions
- Friction (flat or V) belt on the point of slip — the capstan equation gives the maximum tension ratio, so it sizes the minimum grip you need, not the running tension of a loosely run belt.
- Wrap angle θ is taken on the smaller (limiting) pulley and converted to radians; ignores belt mass / centrifugal tension, which reduces grip at high belt speeds.
- For V-belts enter an effective μ (μ / sin(½ · groove angle)); the formula is otherwise identical. Add an installation tension allowance on top of these minimum strand tensions.