Pavements & traffic · Traffic & intersections
Signalised intersection: cycle, green splits and delay calculator
Fixed-time signals with one critical movement per phase. Flow ratios y = q/s give the intersection flow ratio Y and Webster's optimum cycle Co = (1.5L + 5)/(1 − Y); effective greens are split in proportion to y. Each phase gets its degree of saturation, Webster average delay, average back of queue (and its length over the lanes) and level of service.
Standard: Webster (1958) optimum cycle and delay · Austroads Guide to Traffic Management Part 9 · HCM signal LOS by control delay
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Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Phases: name, critical flow q (veh/h), saturation flow s (veh/h), lost time (s), lanes | N–S through, 820, 3600, 5, 2 E–W through, 610, 3400, 5, 2 N–S right turns, 240, 1750, 4, 1 | |
| Cycle time (0 = Webster optimum) | 0 | s |
| Minimum / maximum cycle | 40 | s |
| Maximum cycle | 140 | s |
| Queue storage per vehicle | 7 | m |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Intersection flow ratio Y | 0.544 | |
| Total lost time L | 14 | s |
| Webster optimum cycle Co | 57.1 | s |
| Cycle used | 60 | s |
| N–S through: g 19.2 s · x 0.71 | delay 19.8 s · queue 42 m · LOS B | |
| E–W through: g 15.2 s · x 0.71 | delay 22.8 s · queue 32 m · LOS C | |
| N–S right turns: g 11.6 s · x 0.71 | delay 30.1 s · queue 26 m · LOS C | |
| Average delay (flow-weighted) | 22.4 | s |
| Intersection level of service | C |
- ✓ Y < 0.9 (spare capacity) — 0.54
- ✓ Every phase x ≤ 0.9 (practical degree of saturation) — 0.71
- ✓ Intersection LOS D or better — C
Method, formulas and assumptions
- y = q/s; Y = Σy; L = Σ lost times; Co = (1.5L + 5)/(1 − Y) rounded up to 5 s and limited to the minimum/maximum cycle.
- Effective green g = (C − L)·y/Y; capacity s·g/C; degree of saturation x = q/(s·g/C).
- Webster delay d = C(1 − λ)²/[2(1 − λx)] + x²/[2q(1 − x)] − 0.65(C/q²)^⅓·x^(2 + 5λ); average back of queue ≈ q·r/(1 − q/s).
- LOS by delay: A ≤ 10, B ≤ 20, C ≤ 35, D ≤ 55, E ≤ 80 s. Use SIDRA for design.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.