Saturation Flow
Calculate the saturation flow of a signalized approach, S = S₀ × N, multiplying the base saturation flow per lane S₀ (vehicles/h per lane, typically ~1800–1900) by the number of lanes N. The result, in vehicles/h, is the maximum rate of vehicles that can cross the stop line if the signal stayed green continuously and a queue existed — the queue discharge rate during green. It is a central parameter in signal design and intersection capacity, adjusted by lane width, grade, turning and parking factors. Enter the base saturation flow per lane and the number of lanes.
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Saturation flow
Saturation flow is one of the most important parameters in traffic signal operation: it is the maximum rate at which vehicles can cross the stop line of an approach if the signal stayed green continuously and a queue were always present. In other words, it is the queue discharge rate during green. Picture a signal turning green: the first vehicles pull away from rest and accelerate (with some start-up lost time), but the queue soon settles into a steady discharge rhythm — that rhythm, in vehicles per hour of green, is the saturation flow. In its simplified form, S = S₀ × N, multiplying the base saturation flow per lane S₀ (typically 1800–1900 veh/h per lane, matching a saturation headway of roughly 1.9–2.0 s between vehicles in the queue) by the number of lanes N on the approach. In practice the base value gets corrected by a series of adjustment factors that cut capacity: narrow lane width, grade (upgrades slow the start-up), left and right turns (which demand maneuvering), curbside parking, bus stops, pedestrian activity and heavy vehicles. Saturation flow is the central ingredient in computing the capacity of a signalized approach: capacity = saturation flow × (green time ÷ cycle time). Underestimating it yields signals with too little green and queues that keep growing. Enter the base saturation flow per lane and the number of lanes.
Related Tools
Average Headway
Calculate the average headway (time interval between successive vehicles), h = 3600 ÷ q, dividing 3600 seconds by the flow rate q (vehicles/h). The result, in seconds, is the average time between two consecutive vehicles passing a point. Headway is the inverse of flow: the higher the traffic volume, the shorter the intervals. It is a central concept of traffic flow theory, used in signal design, capacity analysis and car-following models. The smallest safe headway defines the maximum capacity of a lane. Enter the flow rate.
Peak Flow Rate (PHF)
Calculate the peak flow rate of a roadway, q = V ÷ PHF, dividing the hourly volume V (vehicles/h) by the peak hour factor PHF (between 0 and 1, the ratio of the hour's volume to four times the busiest 15-minute volume). The result, in vehicles/h, is the equivalent flow rate of the busiest 15-minute period — always greater than or equal to the hourly volume, since traffic does not arrive uniformly. It is the design flow used in capacity and level-of-service analysis by the HCM, since sizing by the hourly average would underestimate the peaks. Enter the hourly volume and the peak hour factor.
Volume/Capacity Ratio (V/C)
Calculate the volume/capacity ratio (degree of saturation), X = V ÷ C, dividing the traffic volume V by the capacity C of the road or intersection. The dimensionless result measures the road's utilization: X near 0 indicates a free road; X = 1 means the road operating exactly at capacity; X > 1 indicates demand above capacity, with growing queues and congestion. The V/C ratio is the main indicator to classify the level of service (LOS A to F) and identify bottlenecks. Values above 0.85–0.90 already indicate near-saturation operation. Enter the volume and the capacity.
Signal Cycle Time (Webster)
Calculate the optimum signal cycle time by Webster's formula, C = (1.5·L + 5) ÷ (1 − Y), from the total lost time per cycle L (seconds) and the sum of critical flow ratios Y (flow/saturation flow of each phase). The result, in seconds, is the cycle that minimizes total vehicle delay at the intersection. Lost time includes the intergreen intervals and start-up; Y must be less than 1 (otherwise the intersection is saturated and the cycle tends to infinity). It is the fundamental formula for designing isolated signals. Enter the total lost time and the sum of flow ratios.
Equivalent Flow (PCE)
Calculate the equivalent flow in passenger car equivalents (PCE), q = Q_cars + Q_heavy × E, adding the car flow to the heavy-vehicle flow multiplied by the equivalence factor E (how many passenger cars each truck or bus equals in road occupancy — typically 1.5 to 3.0). The result, in PCE/h, converts a mixed traffic stream into an equivalent homogeneous one, allowing volumes to be compared and the capacity of roads with different traffic compositions to be computed. Heavy vehicles occupy more space and accelerate more slowly, especially on grades. Enter the car flow, the heavy-vehicle flow and the equivalence factor.
Space Mean Speed
Calculate the space mean speed of two vehicles by the harmonic mean, v_s = 2 ÷ (1/v₁ + 1/v₂), from the individual speeds v₁ and v₂. The result, in the same unit as the speeds, is the harmonic mean — not the arithmetic — which is the correct way to compute the mean speed of a traffic stream when observing a road section (average over space). Space mean speed is always less than or equal to the time mean speed (the arithmetic mean observed at a point), because it gives more weight to slow vehicles, which spend more time in the section. It is the speed used in the fundamental equation q = k·v. Enter the two speeds.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.