Signal Cycle Length (Webster) Calculator

Work out signal cycle length (webster) instantly with clear inputs, formula shown and shareable results.

About Signal Cycle Length (Webster) Calculator

Webster's optimum cycle length, (1.5 L + 5) / (1 - Y), minimises total delay. L is the lost time per cycle from start-up and clearance, and Y is the sum of the critical flow to saturation flow ratios across phases. As Y approaches one the cycle length rises steeply, which is why heavily loaded intersections need long cycles and suffer long waits.

Formula

Webster optimum cycle

C = (1.5 L + 5) / (1 - Y)

L: Total lost time per cycle
Y: Sum of critical flow ratios

Worked example

With the default values below, Signal Cycle Length (Webster) Calculator returns Optimum cycle length of 76.7. Change any input above and every figure here is recalculated in your browser.

Inputs used

Total lost time per cycleminimum 1 s: 12 s
Sum of critical flow ratiosaccepts 0.01–0.98: 0.7

Results

Optimum cycle length: 76.7 s
Practical cycle length, rounded to 5 seconds: 80 s
Total effective green available: 68.0 s
Intersection capacity utilisation: 70.00% %

Step by step

1Values used
2Webster optimum cycle
3Optimum cycle length= 76.7 s
4Practical cycle length, rounded to 5 seconds= 80 s
5Total effective green available= 68.0 s
6Intersection capacity utilisation= 70.00 %

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Signal Cycle Length (Webster) figure worked out?

C = (1.5 L + 5) / (1 - Y). Webster's optimum cycle length, (1.5 L + 5) / (1 - Y), minimises total delay.

Is a longer cycle always better for capacity?

Up to a point. Longer cycles reduce the proportion of time lost to changeovers but increase delay for every stopped vehicle, and beyond about 120 seconds pedestrian compliance and queue storage become the binding problems.

What values do I need to enter?

This calculator takes 2 inputs: Total lost time per cycle, Sum of critical flow ratios. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.