Traffic Signal Timing Calculator
Determine the optimal signal cycle length and green time splits for a two-phase intersection. Used by traffic engineers when designing or re-timing signals to minimize delay and prevent overflow queuing.
Last updated: September 2026
Formula below · 2 sources (asce.org, Wikipedia) · Updated Sep 2026
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About this calculator
This calculator uses Webster's optimal cycle length formula, a standard method in traffic engineering. The formula is: C = (1.5 × L + 5) / (1 − Y), where C is the cycle length in seconds, L is the total lost time per cycle (two phases here, so L = 2 × the lost time per phase), and Y is the total flow ratio — the sum of approach volumes divided by the saturation flow rate for each phase. The saturation flow rate represents the maximum vehicles per hour that can pass through the stop line under ideal conditions. When Y approaches 1.0, the intersection nears capacity and cycle lengths grow very long. Lost time accounts for start-up lag and end-of-green clearance at each phase, typically 3–5 seconds per phase. This calculator assumes a two-phase signal in which each entered volume is the two-way total for that street, split evenly over one lane per direction, so Y = (NS + EW) / (2 × saturation flow). Effective green time for each phase is then (C − L) × y_i / Y. If Y reaches 1, the intersection is over capacity and no cycle length works.
How to use
Suppose a north-south volume of 600 vph, east-west volume of 400 vph, a saturation flow of 1800 vph/lane, and 4 seconds of lost time per phase (total lost time L = 8 s). First compute Y = (600 + 400) / (1800 × 2) = 1000 / 3600 = 0.278. Then apply Webster's formula: C = (1.5 × 8 + 5) / (1 − 0.278) = 17 / 0.722 ≈ 23.5 seconds. This is the optimal cycle length. Effective green: (23.5 − 8) = 15.5 s to share; north-south y = 600 / 3600 = 0.167, so it gets 15.5 × 0.167 / 0.278 ≈ 9.3 s and east-west ≈ 6.2 s. Webster’s optimum is often shorter than practical minimums (pedestrian crossing times), so cycles below about 40-60 s are usually lengthened in practice. The defaults (800 and 600 vph, 4 s per phase) give Y = 0.389 and C = 17 / 0.611 ≈ 27.8 s.
Frequently asked questions
What is Webster's optimal cycle length formula used for in traffic engineering?
Webster's formula calculates the signal cycle length that minimizes average vehicle delay at an isolated intersection. It balances the time lost during phase transitions against the efficiency gained by longer green periods. The formula works best for under-saturated intersections where total flow ratio Y is below 0.85. Beyond that threshold, delay increases sharply and the intersection is nearing capacity.
How does saturation flow rate affect traffic signal timing calculations?
Saturation flow rate is the maximum number of vehicles that can discharge through a lane in one hour under continuous green, typically 1,600–1,900 vph/lane for urban roads. A higher saturation flow rate means more capacity per lane, which lowers the flow ratio Y and allows shorter, more efficient cycle lengths. Factors like lane width, grade, parking, and turning movements all reduce the effective saturation flow rate below the ideal value.
When should a traffic engineer recalculate signal timing for an intersection?
Signal timing should be re-evaluated whenever traffic volumes change by more than 10–15%, after major land use developments nearby, or as part of a regular retiming program every 3–5 years. Outdated timing plans lead to unnecessary delay, increased emissions, and overflow queuing. Modern adaptive signal control systems recalculate timing continuously, but Webster's method remains valuable for initial design and manual audits.