How to use the string light length calculator
- Enter the span between supports and the sag at the middle of each swag, both in feet.
- Enter the number of swags, which is one fewer than the number of supports.
- Choose the shape, catenary for a hanging chain or parabola for a flat arch, and set the extra length at each support.
- Enter the length of one strand to see how many strands to buy. Open the advanced options to count bulbs from the spacing.
Formula
Straight line (no sag): length = span
Parabola: L = 1/2 sqrt(s^2 + 16 d^2) + s^2 / (8 d) x asinh(4 d / s)
Catenary: y = a (cosh(x / a) - 1) with d = a (cosh(s / 2a) - 1); L = 2 a sinh(s / 2a)
Total = swags x L + extra x (swags + 1)
Strands = total / strand length, rounded up
s is the span and d the sag. The catenary parameter a is found by solving its sag equation numerically. For shallow sags both curves are almost the same.
Three swags across a patio
Each swag spans 20 ft and sags 2 ft. A hanging chain of that shape is 20.52 ft long, only 0.52 ft or 2.6% more than the straight span. With three swags and 1 ft of slack at each of the 4 supports, the total is 3 x 20.52 + 4 = 65.57 ft, so two strands of 48 ft are needed with 30.43 ft to spare.
A deeper sag shows the two shapes separating. For a 30 ft span with a 6 ft sag the parabola is 32.95 ft and the catenary is 32.99 ft. At 20 ft with a 10 ft sag they are 29.58 ft and 29.92 ft.
Why sag adds so little length
A swag that sags 10% of its span is only about 2.6% longer than the straight line between the supports. The length grows with the square of the sag, so doubling the sag roughly quadruples the extra length. That is why a small change in how tight you pull the line changes the length needed by only a few inches, but a deep, droopy swag needs much more.
A strand of lights hanging under its own weight takes the shape of a catenary, the curve of a hanging chain. A parabola is the shape of a suspension bridge cable loaded evenly across the span. The two agree closely for shallow sags, which is why many guides use the simpler parabola.
Buying and hanging
Round the number of strands up and keep a little extra for hooks and the plug end. The extra length per support covers loops around hooks and any lead to an outlet. Check the maker's limit on how many strands can be joined and the total wattage, and use outdoor-rated products and outlets outdoors.
For power and lighting questions, see the circuit load calculator and the lighting lumens calculator. To work out spacing for recessed fixtures instead, see the recessed light spacing calculator, and the pythagorean theorem calculator for diagonal runs.
Assumptions and limits
- Every swag has the same span and sag, with supports at the same height.
- The strand hangs freely under its own weight, with no extra clips along the run.
- The extra length per support is an example (1 ft) for hooks and loops.
- A strand length is the lit and cord length together, as stated by the maker, and is a single value for all strands.
Frequently asked questions
Should I use the catenary or the parabola?
Use the catenary for lights that hang freely, since that is the true shape of a flexible line under its own weight. The parabola is a good stand-in for shallow sags, and the page shows both so you can see how small the gap is.
How is sag measured?
It is the vertical drop from the line joining the two supports to the lowest point of the swag. If the supports are at the same height, that is the distance below the attachment points.
Why include extra length at each support?
Lights are wrapped around hooks or tied to poles, which uses a foot or so at each end, and the plug end needs a lead to an outlet. Leaving it out is the usual reason a run turns out slightly short.
Can I connect strands end to end?
Often yes, up to a limit set by the maker and by the load on the cord. Check the product label for the maximum number and the total watts before planning a long chain.