Tension Calculator

Line Length
Sag / Deflection
Body Weight / Load
Approximation
— kN — kgf — lbf
Exact
— kN — kgf — lbf

The Math

Before we begin, it's worth noting that the value calculated with these formulas is independent of the webbing type. The reason for this is because we are calculating the value of the force when a person or weight is applied to the line in the middle. At this moment in time, there is theoretically no movement in the system. Line dynamics do not come into play in this scenario. When there is no one on the line, the force in the system depends greatly on the material type and how much it elongates at a given force (stress-strain curve). We are not calculating this value though.

The setup

To begin, let's take a look at a diagram of what a slackline looks like when someone is standing in the middle.

L S B TForce Θ WForce
  • L  =  Line Length
  • S  =  Line Sag
  • B  =  Half of line length after standing on the line
  • Θ  =  Angle between original line and line after standing on it
  • TForce  =  Tension in the line
  • WForce  =  Weight of the slackliner

Exact tension

From the above, we are trying to find the value of TForce. Keep in mind, your body weight is shared between the two anchors. With that information, we can deconstruct the above diagram into a simple right triangle, from which we can compute the tension easily.

B TForce S WForce / 2 L / 2 Θ

From this diagram we can see directly that:

B S = T W / 2

We can also derive the following via the Pythagorean theorem:

B = S 2 + ( L / 2 ) 2

Now using the classic "two equations, two unknowns" trick, we can solve for T:

T = W · B 2S = W · S 2 + ( L / 2 ) 2 2S

The approximation

That gives us the exact value for the tension — but there's a much easier way to estimate it. Because Θ is extremely small for any line where length far exceeds sag, the value of B is almost identical to L/2. So we can substitute one for the other in the above equations:

B S = T W / 2 ⇒ L / 2 S = T W / 2

That leaves us with only one unknown — T. Solving for it:

T = W · L 4S

That's the approximate force on the slackline. The approximation holds for any setup where the line length is much greater than the sag. When you start getting into rodeolines or super-loose lines (sag-to-length ratio more than 1/5), you'll see a noticeable difference between the approximate and exact values.