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Traffic Signal Timing Calculator — Yellow, All-Red, Webster Cycle & Splits

Time a pretimed signal from start to finish: the ITE yellow change and red clearance intervals for the approach speed and grade, pedestrian walk and clearance times, Webster's optimum cycle length and the HCM minimum cycle, then green splits allocated by critical flow ratio with the resulting capacity, volume-to-capacity ratio and uniform delay for each phase.

Yellow change and red clearance (ITE)

Approach speed, vmi/h (85th percentile or posted)

Approach grade, G% (+ uphill, − downhill)

Perception–reaction time, ts

Deceleration rate, aft/s²

Intersection width, Wft (stop line to far side of last conflicting lane)

Vehicle length, Lft

Approach speed—ft/s

Yellow change interval, Y—s (use — s)

All-red clearance, AR—s (use — s)

Pedestrian timing (MUTCD 4I.06)

Crosswalk lengthft (curb to far side of traveled way)

Walking speedft/s

Walk intervals (minimum 7 s typical)

Pedestrian clearance (flashing DON'T WALK)—s

Walk + clearance—s

Cycle length and splits (Webster)

Lost time per phase, t_Ls (start-up + clearance lost time)

Target critical v/c, X_cfor HCM minimum cycle

Cycle length overrides — blank = Webster C_o rounded up to 5 s

Phase	y = v/s	Eff. green g	Displayed G	Capacity	v/c	Delay d₁ (s/veh)
1	—	—	—	—	—	—
2	—	—	—	—	—	—
3	—	—	—	—	—	—
4	—	—	—	—	—	—

Enter one row per phase using the critical (highest v/s) lane group of that phase, per lane. Leave a row blank to drop the phase.

Sum of critical flow ratios, ΣY——

Total lost time, L = n·t_L—s

Webster optimum cycle, C_o—s

HCM minimum cycle, C_min—s

Cycle used, C—s

Critical v/c, X_c = ΣY·C/(C − L)——

Pedestrian check—

Yellow change interval and all-red clearance (ITE kinematic method):

$$ Y = t + \frac{1.467\,v}{2a + 2gG}, \qquad AR = \frac{W + L}{1.467\,v} $$

Webster's optimum cycle and the HCM minimum cycle:

$$ C_o = \frac{1.5L + 5}{1 - \sum y_i}, \qquad C_{min} = \frac{L\,X_c}{X_c - \sum y_i} $$

Green split in proportion to critical flow ratios, capacity, and uniform delay:

$$ g_i = \frac{y_i}{\sum y_i}\,(C - L), \qquad c_i = s_i\,\frac{g_i}{C}, \qquad d_1 = \frac{0.5\,C\,(1 - g/C)^2}{1 - \min(1, X)\,g/C} $$

v approach speed (mi/h; 1.467 converts to ft/s) · g = 32.2 ft/s² · G grade as a decimal · y_i = v/s for the critical lane group of phase i · L total lost time per cycle · effective green g = displayed green G + Y + AR − t_L.

The timing sequence

A pretimed signal is designed in three steps. First, the change interval (yellow) and clearance interval (all-red) come from the approach speed and intersection geometry, so a driver who cannot stop comfortably can clear the intersection. Second, the cycle length is chosen from the critical flow ratios and the lost time. Third, the effective green left over after lost time is split among the phases. Pedestrian timing then sets a floor on each phase that carries a concurrent crosswalk.

Yellow change interval, Y (s), ITE formula with t = 1.0 s and a = 10 ft/s²
Speed (mi/h)	−4% grade	−2% grade	Level	+2% grade	+4% grade
25	3.1	3.0	2.8	2.7	2.6
30	3.5	3.4	3.2	3.1	2.9
35	3.9	3.7	3.6	3.4	3.3
40	4.4	4.1	3.9	3.8	3.6
45	4.8	4.5	4.3	4.1	3.9
50	5.2	4.9	4.7	4.4	4.2
55	5.6	5.3	5.0	4.8	4.6

MUTCD requires a yellow of 3 to 6 s. Values the formula pushes above 6 s are usually held at 6 s with the extra time added to the all-red interval. Local agencies sometimes use 0.9 s for t or a 15th-percentile speed for the all-red calculation; enter their values if they differ.

Cycle length

Webster's formula balances two effects: short cycles lose a larger share of time to start-up and clearance, while long cycles make vehicles wait through long reds. It assumes random arrivals and is reliable when ΣY is below about 0.85. The HCM minimum cycle, C_min = L·X_c/(X_c − ΣY), is the shortest cycle that keeps the critical v/c at the target X_c — useful as a lower bound. Practical cycles fall between 60 and 120 s, with 150 s an upper limit at busy intersections.

Uniform delay d₁ is the first term of the HCM control-delay equation. It covers delay from the red time with evenly spaced arrivals; random and oversaturation delay (d₂, d₃) and progression adjustments are not included, so actual delay will be somewhat higher, especially as v/c approaches 1.

Worked example

Three-phase intersection at 45 mi/h

Given: level approaches at 45 mi/h, W = 60 ft, L = 20 ft. Critical lane flows 650, 420 and 250 veh/h with saturation flows 1,800, 1,800 and 1,700 veh/h/ln. Lost time 4 s per phase. 60-ft crosswalks.

Y = 1.0 + 66.0/(2 × 10) = 4.3 s (time 4.5 s). AR = (60 + 20)/66.0 = 1.2 s (time 1.5 s).

y = 650/1,800 = 0.361; 420/1,800 = 0.233; 250/1,700 = 0.147. ΣY = 0.742. L = 3 × 4 = 12 s.

C_o = (1.5 × 12 + 5)/(1 − 0.742) = 89.0 s → use 90 s. C_min at X_c = 0.90 is 68 s.

Effective green 90 − 12 = 78 s: g = 38.0, 24.5, 15.5 s. Displayed green G = g − 4.3 − 1.2 + 4 = 36.5, 23.0, 14.0 s. Every critical lane group runs at v/c = 0.856; uniform delay 23.5, 31.0 and 36.2 s/veh.

Pedestrians: 7 + 60/3.5 = 24.1 s. Phase 3 offers only 14.0 + 4.3 + 1.2 = 19.5 s, so its crosswalk needs a pushbutton-actuated longer phase or a longer cycle.

90-s cycle, splits 36.5 / 23.0 / 14.0 s green + 4.3 s yellow + 1.2 s all-red each.

Limits of this tool

Pretimed, isolated signal. Actuated control, coordination and offsets are outside its scope.
One yellow and all-red setting is applied to every phase. If phases have different speeds or widths, time them separately and adjust each displayed green.
Saturation flow must be supplied; the HCM adjusts a 1,900 pc/h/ln base for lane width, heavy vehicles, grade, parking, turns and area type.

Frequently asked questions

How do you calculate the yellow change interval?

The ITE kinematic formula is Y = t + 1.467v / (2a + 2gG), with t the perception-reaction time (1.0 s), v the approach speed in mi/h, a the deceleration rate (10 ft/s²), g = 32.2 ft/s² and G the grade as a decimal (negative downhill). At 45 mi/h on level ground Y = 1.0 + 66/20 = 4.3 s. MUTCD limits yellow to 3–6 s.

How do you calculate the all-red clearance interval?

AR = (W + L) / (1.467v), the time to travel from the stop line past the far conflict point: W is the intersection width and L the vehicle length (about 20 ft). For W = 60 ft at 45 mi/h, AR = 80 / 66 = 1.2 s. MUTCD caps the red clearance at 6 s.

What is Webster's optimum cycle length?

Webster (1958) found that delay is minimized near Co = (1.5L + 5)/(1 − ΣY), where L is total lost time per cycle and ΣY is the sum of critical flow ratios v/s. Delay rises slowly for cycles between about 0.75Co and 1.5Co, so the result is usually rounded up to the next 5 s.

How are green times split between phases?

The effective green available, C − L, is divided in proportion to each phase's critical flow ratio: gi = (yi/ΣY)(C − L). That gives every critical lane group the same volume-to-capacity ratio. Displayed green is then the effective green minus yellow and all-red plus the lost time: G = g − Y − AR + tL.

What is lost time at a signal?

Start-up lost time is the extra time the first few queued vehicles need to accelerate (about 2 s). Clearance lost time is the part of yellow and all-red not used by vehicles (about 2 s). Their sum per phase, commonly taken as 4 s, is time in the cycle that serves no traffic.

How long should the pedestrian clearance interval be?

MUTCD 4I.06 sets pedestrian clearance (flashing DON'T WALK) to the crossing distance divided by a 3.5 ft/s walking speed, after a walk interval of at least 7 s (4 s where pedestrian volumes are low). A 60-ft crossing needs 17.1 s of clearance, 24.1 s in total.

References: Institute of Transportation Engineers (2020), Guidelines for Determining Traffic Signal Change and Clearance Intervals. FHWA, Manual on Uniform Traffic Control Devices, 11th ed. (2023), Ch. 4F and 4I. Webster, F.V. (1958), "Traffic signal settings," Road Research Technical Paper 39, HMSO. Transportation Research Board, Highway Capacity Manual, 7th ed. (2022), ch. 19. FHWA, Signal Timing Manual, 2nd ed., NCHRP Report 812 (2015).

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