Webster Signal Design Calculator
A two-phase signal with critical flows of 500 and 600 PCU/h (saturation 1800 PCU/h) and 12 s lost time needs an optimum cycle of 59.1429 s.
Typically 2 s start-up lost time plus all-red per phase.
59.1428571428572 s
Full answer, then cut to fewer decimals (not rounded):
- 59.1428571428572 s
- 59.142857142857 s
- 59.14285714285 s
- 59.1428571428 s
- 59.142857142 s
- 59.14285714 s
- 59.1428571 s
- 59.142857 s
- 59.14285 s
- 59.1428 s
- 59.142 s
- 59.14 s
- 59.1 s
- Y = Σ y
- 0.6111111111
- Effective green available C₀ − L
- 47.14285714 s
| Phase | y = q/s | Effective green (s) |
|---|---|---|
| 1 | 0.277778 | 21.4286 |
| 2 | 0.333333 | 25.7143 |
Step-by-step solution
- y = q/s for each phase: 0.277778, 0.333333
- C₀ = (1.5L + 5) / (1 − Y) = (1.5 × 12 + 5) ÷ (1 − 0.6111111111) = 59.14285714 s
Webster Signal Design Formula
C₀ = (1.5L + 5) / (1 − Y)
Y = Σ q/s over critical phases; green gᵢ = (C₀ − L) yᵢ/Y
Worked Example
A two-phase signal with critical flows of 500 and 600 PCU/h, saturation flow 1800 PCU/h and 12 s lost time:
- y = q/s for each phase: 0.277778, 0.333333
- C₀ = (1.5L + 5) / (1 − Y) = (1.5 × 12 + 5) ÷ (1 − 0.6111111111) = 59.14285714 s
Effective green available C₀ − L: 47.14285714 s
| Phase | y = q/s | Effective green (s) |
|---|---|---|
| 1 | 0.277778 | 21.4286 |
| 2 | 0.333333 | 25.7143 |
GATE tip
Round the cycle up to the next 5 s in practice, but give the unrounded C₀ in a NAT answer.
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Frequently asked questions
What happens when Y approaches 1?
The cycle length grows without limit: the junction is near saturation and needs more capacity, not longer cycles.
Is the computed green time the displayed green?
It is effective green; displayed green = effective green + lost time − amber, per phase.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Webster Signal Design Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/webster-signal-calculator/
IEEE
Scientific Converters, "Webster Signal Design Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/webster-signal-calculator/