Intersection Delay Calculator

Work out intersection delay instantly with clear inputs, formula shown and shareable results.

About Intersection Delay Calculator

Signal delay has two parts. Uniform delay assumes vehicles arrive evenly and depends on the green to cycle ratio; incremental delay accounts for random arrivals and oversaturation and grows sharply as the degree of saturation approaches one. Level of service at signals is graded on average control delay, with A at ten seconds and F beyond eighty.

Formulas

Uniform delay

d1 = 0.5 C (1 - g/C)² / (1 - (g/C) x)

Degree of saturation

x = arrival flow / (saturation flow x g/C)

Worked example

With the default values below, Intersection Delay Calculator returns Average delay per vehicle of 27.22. Change any input above and every figure here is recalculated in your browser.

Inputs used

Cycle lengthminimum 20 s: 90 s
Effective green for the movementminimum 1 s: 40 s
Arrival flowminimum 1 veh/h: 600 veh/h
Saturation flowminimum 1 veh/h: 1,800 veh/h

Results

Average delay per vehicle: 27.22 s
Uniform delay component: 20.83 s
Degree of saturation: 0.7500
Level of service: C — average control delay 27 seconds

Step by step

1Values used
2Uniform delay
3Degree of saturation
4Average delay per vehicle= 27.22 s
5Uniform delay component= 20.83 s
6Degree of saturation= 0.7500
7Level of service= C — average control delay 27 seconds

Assumptions and limits

The result is derived only from the 4 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 4 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 Intersection Delay figure worked out?

d1 = 0.5 C (1 - g/C)² / (1 - (g/C) x). Signal delay has two parts.

Why does delay explode near capacity?

Because randomness matters. Even when average demand equals capacity, some cycles receive more arrivals than can discharge, and the residual queue carries forward and compounds.

What values do I need to enter?

This calculator takes 4 inputs: Cycle length, Effective green for the movement, Arrival flow, Saturation flow. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.