Calculation
T = W / (n · sin θ)
The shallower the sling angle to horizontal, the more tension per leg rises.
T = W / (n·sin θ)
Tension per leg for an angled sling
The shallower the sling angle to horizontal, the more tension per leg rises.
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Result
Select a target and calculate.
Understand the inputs
- Tension per leg T — Force carried by a single sling leg.
- Total load (weight force) W — Total weight force of the lifted load, not its mass.
- Number of load-bearing legs n — Number of sling legs sharing the load.
- Sling angle θ — Angle between the sling leg and the horizontal.
Example
A 100 kN total load on 2 legs at 45° gives about 70.7 kN tension per leg.
Assumptions and limits
Symmetric load sharing across all legs; shock loads and lifting dynamics are excluded.
Understand Tension per leg for an angled sling
This calculator finds the missing quantity among tension per leg T, total load W, leg count n and sling angle θ from the other three. Using an official sling-angle factor table, it shows why a shallow sling angle drastically raises tension per leg — an effect easy to underestimate when lifting with multi-leg slings.
What does this quantity describe?
In a multi-leg sling, total load first splits evenly across all load-bearing legs; a sling angle away from vertical additionally raises actual tension per leg by a factor of 1/sin θ: T = W/(n·sin θ).
A sling-angle comparison table shows the effect concretely: at 90° (vertical) the load factor is 1.0, at 60° it's already 1.155, at 45° it's 1.414, and at exactly 30° it's 2.0 — at a 30° sling angle, each leg therefore carries the full weight of the load even though two legs are lifting together. Sling angles below 30° are generally considered not recommended for this reason.
Formula and variables
T = W / (n · sin θ)
T = W / (n · sin θ)W = T · n · sin θn = W / (T · sin θ)θ = arcsin(W / (T·n))
| Symbol / input | Meaning |
|---|---|
| Tension per leg T | Force carried by a single sling leg. |
| Total load (weight force) W | Total weight force of the lifted load, not its mass. |
| Number of load-bearing legs n | Number of sling legs sharing the load. |
| Sling angle θ | Angle between the sling leg and the horizontal. |
Choose the inputs correctly
Enter three of the four quantities to find the fourth. Use total weight force for W, not the load's mass; θ is the angle between the sling leg and horizontal, not the angle between two legs.
How to use the calculator
Select the target quantity and enter the three known values with units. Compare the result against the sling's rated capacity at this angle afterward, since rated capacity falls as angle gets shallower.
Worked example
Given W = 100 kN, n = 2 legs and θ = 45°, substitution gives T = 100/(2·sin 45°) ≈ 70.7 kN per leg.
Understand the result and units
A tension of 70.7 kN per leg sits well above the simple load share of 50 kN (total load divided by leg count), because the 45° angle raises tension per leg by a factor of 1.414. This elevated tension, not the simple load share, is what governs sling selection.
Forces in newtons (N) or kilonewtons (kN), sling angle in degrees. Leg count n is a dimensionless integer.
Why is a shallow sling angle dangerous?
As sling angle falls, the load factor 1/sin θ grows nonlinearly: from 90° to 45°, tension per leg only roughly moderately increases (factor 1.414), but from 45° to 30° it already rises considerably more (factor 2.0), and below 30° it climbs very quickly further. A too-shallow sling angle can therefore exceed a sling's rated capacity at only a modest change in setup, even though the lifted load itself stays the same — one reason sling angles below 30° are considered not recommended in practice.
Typical applications
The formula is used to select webbing slings, chains and wire ropes for multi-leg bridle hitches, plan load distribution for irregularly shaped loads, and in rigging safety training.
Assumptions, limits and common mistakes
The formula assumes symmetric load sharing across all legs and a static, at-rest load. For asymmetric load centers of gravity, unequal leg lengths, or dynamic loads (lifting, braking), real leg tensions deviate from this idealized value and need separate analysis.
Common mistake: Do not confuse sling angle with the angle between two opposing legs — what matters is always the angle of each individual leg to horizontal. Also, do not substitute the total load as a mass into the tension formula without first converting it to a weight force using gravitational acceleration.
Frequently asked questions
Why does tension per leg rise at a shallower sling angle?
Because part of the leg's force splits into a horizontal component that does no lifting work. The shallower the angle to horizontal, the larger the total force in the leg must be to carry the same vertical load share.
What sling angle counts as a lower limit?
Angles below 30° to horizontal are generally considered not recommended, since tension per leg is already at least double that of a vertical hitch there and rises quickly further as the angle keeps falling.
Should I enter the load as mass or weight force?
As weight force (mass multiplied by gravitational acceleration), since the formula is a force balance, not a mass balance.