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.
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 (sum of 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. Green time for each approach is then split proportionally to its share of Y.
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. Green time for north-south = 23.5 × (600/1800) / 0.278 ≈ 28 s (after subtracting lost time and scaling). Adjust splits proportionally to each phase's flow ratio.
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.