Traffic Signal Timing Calculator
Calculate green, yellow, and all-red phase timing for traffic signal intersections. Enter values for instant results with step-by-step formulas.
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Where t = perception-reaction time (s), v = approach speed (ft/s), a = deceleration rate (ft/s^2), W = intersection width (ft), L = vehicle length (ft), Co = optimal cycle length, L = total lost time, Y = sum of critical flow ratios.
Last reviewed: December 2025
Worked Examples
Example 1: Yellow and All-Red Timing for 45 mph Approach
Example 2: Two-Phase Green Split by Volume
Background & Theory
The Traffic Signal Timing Calculator applies the following established principles and formulas. Structural and construction engineering is governed by fundamental load analysis, material science, and regulatory standards that ensure the safety and durability of built structures. The primary distinction in load analysis is between dead loads โ the permanent self-weight of structural elements, finishes, and fixed equipment โ and live loads, which represent variable occupancy, furniture, and environmental forces such as wind and snow. These are combined using factored load equations, such as the ASCE 7 formula U = 1.2D + 1.6L, where D is dead load and L is live load. Concrete mix design is governed by the water-cement (w/c) ratio, which is the primary determinant of compressive strength and durability. A w/c ratio of 0.40โ0.45 typically yields concrete with 28-day compressive strengths of 30โ40 MPa. Common mix ratios by weight for structural concrete are approximately 1 part cement : 1.5โ2 parts sand : 3 parts coarse aggregate. Structural steel is characterized by its yield strength (the stress at which permanent deformation begins, typically 250โ350 MPa for mild steel) and ultimate tensile strength (typically 400โ500 MPa). Mid-span deflection of a simply supported beam under a central point load is given by ฮด = FLยณ / (48EI), where F is force, L is span length, E is Young's modulus, and I is the second moment of area. Building insulation is rated by R-value, a measure of thermal resistance in units of mยฒยทK/W (SI) or ftยฒยทยฐFยทh/BTU (imperial). Higher R-values indicate greater resistance to heat flow. Foundation design depends on the allowable bearing capacity of the underlying soil, which ranges from approximately 75 kPa for soft clay to over 10,000 kPa for bedrock. Drainage gradients for surface water are typically specified as a minimum of 1โ2% slope away from building foundations to prevent hydrostatic pressure and water infiltration.
History
The history behind the Traffic Signal Timing Calculator traces back through the following developments. The history of construction engineering spans thousands of years of accumulated empirical knowledge and, more recently, rigorous scientific analysis. The ancient Egyptians built the Great Pyramid of Giza around 2560 BCE using an estimated 2.3 million stone blocks, demonstrating sophisticated logistics, geometry, and workforce organization. Roman engineers advanced the field dramatically through the use of pozzolanic concrete โ a mixture of volcanic ash, lime, and seawater โ enabling the construction of the Pantheon dome (43.3 m diameter, completed around 125 CE) and a vast network of aqueducts and roads across the empire. Cast iron emerged as a structural material during the Industrial Revolution, first used prominently in the Iron Bridge at Coalbrookdale, England, completed in 1779. Wrought iron and later steel allowed far greater spans and heights. The Eiffel Tower, completed in 1889, demonstrated the structural possibilities of wrought iron at scale and influenced the development of steel-frame skyscraper construction in Chicago and New York. Reinforced concrete was systematically developed by Joseph Monier, a French gardener, who patented iron-reinforced concrete pots and panels in the 1860s, and later by engineers including Franรงois Hennebique who created the first comprehensive reinforced concrete framing system in the 1890s. The 1906 San Francisco earthquake caused widespread devastation and galvanized the engineering profession to develop seismic design provisions. Subsequent earthquakes โ including the 1971 San Fernando and 1994 Northridge events โ drove successive improvements in seismic codes, base isolation technology, and ductile detailing of reinforced concrete and steel frames. Building codes became increasingly standardized in the twentieth century, with the International Building Code (IBC) first published in 2000 providing a unified model code adopted across much of the United States. Building Information Modeling (BIM) emerged in the 2000s as a digital workflow integrating architectural, structural, and MEP design into a unified three-dimensional model, fundamentally changing coordination practices across the industry.
Frequently Asked Questions
Formula
Yellow = t + v/(2a) | All-Red = (W+L)/v | Co = (1.5L+5)/(1-Y)
Where t = perception-reaction time (s), v = approach speed (ft/s), a = deceleration rate (ft/s^2), W = intersection width (ft), L = vehicle length (ft), Co = optimal cycle length, L = total lost time, Y = sum of critical flow ratios.
Worked Examples
Example 1: Yellow and All-Red Timing for 45 mph Approach
Problem: Calculate yellow and all-red intervals for a 45 mph approach speed, 40-foot intersection width, 20-foot vehicle length, level grade.
Solution: Speed = 45 mph = 45 x 1.467 = 66.0 ft/s\nReaction time t = 1.0 s\nDeceleration a = 10 ft/s^2, Grade G = 0\nYellow = t + v/(2a) = 1.0 + 66.0/(2 x 10) = 1.0 + 3.3 = 4.3 s\nAll-red = (W + L)/v = (40 + 20)/66.0 = 0.9 s\nTotal change + clearance = 4.3 + 0.9 = 5.2 s per phase
Result: Yellow: 4.3 s | All-Red: 0.9 s | Total clearance: 5.2 s per phase
Example 2: Two-Phase Green Split by Volume
Problem: Distribute green time for a 90-second cycle with main street volume 800 vph and cross street 400 vph.
Solution: Lost time per phase = 2 s, Total lost = 2 x 2 = 4 s\nEffective green available = 90 - 4 = 86 s\nVolume ratio: Main = 800/(800+400) = 0.667\nVolume ratio: Cross = 400/(800+400) = 0.333\nGreen (main) = 0.667 x 86 = 57.3 s\nGreen (cross) = 0.333 x 86 = 28.7 s\nCapacity main = 1800 x (57.3/90) = 1146 vph\nv/c main = 800/1146 = 0.70 (LOS B)
Result: Green Main: 57.3 s | Green Cross: 28.7 s | v/c Main: 0.70 (LOS B)
Frequently Asked Questions
How is the yellow (change) interval calculated for traffic signals?
The yellow interval is calculated using the ITE (Institute of Transportation Engineers) formula: Y = t + v/(2a + 2gG), where t is the driver perception-reaction time (typically 1.0 second), v is the approach speed in feet per second, a is the comfortable deceleration rate (typically 10 ft/s squared), g is gravitational acceleration (32.2 ft/s squared), and G is the roadway grade as a decimal. For a 45 mph approach on level grade, the yellow interval calculates to approximately 3.6 seconds. The yellow interval ensures that a driver who cannot safely stop at the onset of yellow has enough time to reach the intersection before the signal turns red. Shorter yellow intervals increase red-light running and intersection crashes.
What factors should be considered when setting pedestrian signal timing?
Pedestrian signal timing must provide adequate time for pedestrians to safely cross the street. The Walk interval typically lasts 7 seconds minimum, allowing pedestrians to step off the curb and begin crossing. The flashing Don't Walk interval must be long enough for a pedestrian who started crossing at the end of the Walk phase to reach the far side. This equals the crossing distance divided by the assumed walking speed of 3.5 feet per second for general populations, or 3.0 feet per second near senior centers, schools, or hospitals. For a 40-foot crossing at 3.5 ft/s, the flashing Don't Walk interval is approximately 11.4 seconds. The total pedestrian phase time often constrains the minimum green time, particularly on wide cross streets.
What is signal coordination and how does it reduce travel delay?
Signal coordination, often called a green wave, synchronizes adjacent traffic signals along a corridor so that vehicles traveling at the design speed encounter a series of green signals without stopping. This is achieved by offsetting the start of green at each successive intersection by the travel time between them. The offset equals the distance between intersections divided by the progression speed. Effective coordination can reduce stops by 30 to 50 percent and travel time by 15 to 25 percent along major corridors. However, coordination requires a common cycle length at all intersections, which may not be optimal for individual intersections. Two-way coordination is challenging because the ideal offsets for the two directions may conflict, often requiring compromise solutions.
How does intersection geometry affect signal timing calculations?
Intersection geometry significantly influences multiple aspects of signal timing. Wider intersections require longer all-red clearance intervals, which consume more of the available green time. Skewed intersections increase the effective crossing distance for both vehicles and pedestrians. The number and configuration of lanes determine the saturation flow rate and capacity. Exclusive turn lanes allow protected turn phases without blocking through traffic, but add signal phases that increase cycle length and lost time. Right-turn channelization with acceleration lanes can reduce conflicts and improve capacity. Intersection sight distance affects the required yellow interval, as limited sight distance may necessitate longer perception-reaction times. Modern roundabouts eliminate signal timing entirely but require sufficient space and moderate traffic volumes.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.
References
Reviewed by Daniel Agrici, Founder & Lead Developer ยท Editorial policy