Sag Tension Calculator
Get midspan sag from horizontal tension, or the tension for a measured sag, with the exact catenary or the parabola. Pick an ACSR conductor (Sparrow to Cardinal) to see tension as a percent of rated strength, the NESC ice-and-wind loaded tension and a sag–tension table from cold to hot.
Conductor sag at midspan for a level span is S = w × L² ÷ (8 × H), where w is conductor weight per unit length, L is span length and H is horizontal tension.
Use the Sag Tension Calculator
Span & Conductor Parameters
Height of right tower relative to left tower (≥ 0).
Conductor Deflection Profile
Chord midspan vertical offsetStatic Solution Breakdown
Conductor strength, NESC loading & sag–temperature table
Uses the span, weight and tension from the calculation above as the state at the reference temperature (level-span parabolic change of state).
- Horizontal tension, % RBS
- —
- Max support tension, % RBS
- —
- Unloaded limit check
- —
- Loaded weight (ice + wind + k)
- —
- Loaded tension H / sag
- —
- Loaded % RBS (limit 60%)
- —
| Temperature | Horizontal tension | Midspan sag | % RBS |
|---|---|---|---|
| Pick a conductor or enter area, modulus and expansion. | |||
| District | Radial ice | Wind | Temp | k |
|---|---|---|---|---|
| Heavy | 0.50 in | 4 lb/ft² | 0 °F | 0.30 lb/ft |
| Medium | 0.25 in | 4 lb/ft² | 15 °F | 0.20 lb/ft |
| Light | 0.00 in | 9 lb/ft² | 30 °F | 0.05 lb/ft |
| Warm islands | 0.00 in | 9 lb/ft² | 50 °F | 0.05 lb/ft |
Tension limits (Rule 261H1): 60% RBS loaded; unloaded at 60 °F, 35% initial and 25% final.
| Code word | Dia. (in) | Weight (lb/ft) | RBS (lb) |
|---|---|---|---|
| Sparrow 2 AWG 6/1 | 0.316 | 0.091 | 2,850 |
| Raven 1/0 6/1 | 0.398 | 0.145 | 4,380 |
| Penguin 4/0 6/1 | 0.563 | 0.291 | 8,350 |
| Partridge 266.8 kcmil 26/7 | 0.642 | 0.367 | 11,300 |
| Linnet 336.4 kcmil 26/7 | 0.720 | 0.462 | 14,100 |
| Hawk 477 kcmil 26/7 | 0.858 | 0.656 | 19,500 |
| Drake 795 kcmil 26/7 | 1.107 | 1.093 | 31,500 |
| Cardinal 954 kcmil 54/7 | 1.196 | 1.227 | 33,800 |
Diameter, weight and rated strength from the Southwire ACSR specification; check your own conductor's data sheet.
Standard Unit Definitions & Relationships
- 1 foot = exactly 0.3048 m (NIST SP 811).
- 1 lbf = 4.448222 N; 1 lb/ft = 14.593903 N/m.
- Catenary Constant: $c = H / w$ in length units, indicating the length of conductor whose weight matches horizontal tension.
- Parabolic Departure: Midspan vertical chord sag is $S = \frac{w L^2}{8 H}$ for both level and uniform horizontal projected load inclinations.
- Exact Support Tension: True vector tension at support is $T = \sqrt{H^2 + V^2} = H \cosh((x - x_0)/c)$, never simple scalar addition.
Scope & Engineering Limitations
This calculator isolates static single-span catenary and parabolic mechanics. Field transmission line engineering requires comprehensive rulings:
- Nonlinear conductor stress-strain, creep elongation, and thermal expansion.
- Radial glaze ice, transverse wind pressures, and structural support flexibility.
Quick answer
Conductor sag at midspan for a level span is S = w × L² ÷ (8 × H), where w is conductor weight per unit length, L is span length and H is horizontal tension. Halving the tension doubles the sag. Utilities also keep tension below a share of the rated breaking strength: NESC Rule 261H1 limits are 60% under the rated ice and wind load and, unloaded at 60 °F, 35% initial and 25% final.
Examples
| Span, weight, tension | Midspan sag |
|---|---|
| 300 m, 1.166 N/m, 20 kN | 0.656 m |
| 300 m, 1.166 N/m, 10 kN | 1.312 m |
| 300 ft, 0.5 lb/ft, 2,000 lbf | 2.81 ft |
| 300 ft Drake (1.093 lb/ft), 6,300 lbf (20% RBS) | 1.95 ft |
Enter span, weight and tension, then pick a conductor and NESC district for % RBS, loaded tension and the sag–temperature table.
Summary
Overhead conductors hang in a catenary. For a level span the midspan sag is S = c·(cosh(L/2c) − 1) with c = H/w, which the parabola S = w·L²/(8H) matches closely while sag stays small. This calculator solves sag from tension or tension from sag with either model, handles supports at different heights and draws the profile. Choosing an ACSR conductor fills its weight, diameter and rated breaking strength (RBS) so the tension can be read as a percent of RBS. The NESC panel adds radial ice, wind pressure and the constant k for the heavy, medium, light or warm-islands district and finds the loaded tension with the change-of-state equation, which uses the conductor's area, modulus and thermal expansion; the same equation produces a sag–tension table from cold to hot. It is a linear-elastic, single-span estimate without creep or ruling-span effects, so final designs still need SAG10, PLS-CADD or the utility's own sag charts.
How it works
- Choose the goal: sag from tension, or tension from a measured or target sag.
- Choose the parabolic or exact catenary model and enter span length, conductor weight and tension or sag; add the support height difference for an inclined span.
- Pick an ACSR conductor (or enter your own diameter, rated strength, area, modulus and expansion) to see tension as a percent of rated breaking strength.
- Set the temperature of the entered state and an NESC loading district to get the ice-and-wind loaded weight, tension, sag and percent of RBS.
- Read the sag–tension table to see how sag and tension change between cold and hot conductor temperatures.
Use cases
- Calculate midspan sag for a new distribution or transmission span at a chosen stringing tension.
- Find horizontal tension and percent of rated strength from a field-measured sag.
- Check a span against NESC Rule 261H1 tension limits under heavy, medium or light district loading.
- Make a quick sag–temperature table for stringing at the air temperature on the day.
- Compare parabolic and exact catenary results, including inclined spans on hilly ground.
- Estimate sag and tension for joint-use attachments and clearance checks.