Traffic Signal Timing Calculator
Enter the approach speed, grade, intersection width and crossing distance to get the yellow, all-red and pedestrian times, then the phase volumes to get Webster's cycle length and green split for each phase.
Yellow = t + v ÷ (2a + 2gG) with t = 1 s and a = 10 ft/s², so a 45 mph approach on level ground needs 1 + 66.15 ÷ 20 = 4.31 s, rounded up to 4.4 s of yellow; all-red = (W + L) ÷ v, and pedestrian clearance = crossing distance ÷ 3.5 ft/s.
Use the Traffic Signal Timing Calculator
Intersection Parameters
Typical range: 3–5 s. Default is 4 s/phase.
Used when phase rows are created; each row remains editable.
Enter intersection parameters and click Calculate Timing to see results.
Phase Timing Breakdown
| Phase | Volume (veh/hr) | Sat. Flow | v/s Ratio | Green (s) | % of Cycle | Ped time |
|---|
Cycle Allocation
Formula: Co = (1.5L + 5) / (1 − Y), where L = total lost time, Y = sum of critical flow ratios.
The raw Webster result is rounded up to the next 5-second increment; no arbitrary minimum or maximum is silently imposed.
Ped time: each phase green is compared with walk + pedestrian clearance from the section below. This is conservative: some agencies let the clearance run into the yellow and all-red.
Inputs must represent the critical lane or lane group for each phase. Results are for an isolated, fixed-time, undersaturated planning case; verify pedestrian minimums, clearance, coordination and local standards.
Yellow, all-red and pedestrian timing
- Yellow change (Y)
- —
- All-red clearance (AR)
- —
- Pedestrian clearance
- —
- Walk + clearance
- —
Yellow and all-red times by approach speed
ITE kinematic formula with v = mph × 1.47 ft/s, t = 1.0 s, a = 10 ft/s², g = 32.2 ft/s², rounded up to 0.1 s. All-red for a 60 ft intersection and a 20 ft vehicle. MUTCD guidance: yellow 3–6 s, red clearance up to 6 s. Agencies may use posted, 85th-percentile or posted + 5 mph speeds.
| Speed | Yellow, level (s) | Yellow, +3% up (s) | Yellow, −3% down (s) | All-red (s) |
|---|---|---|---|---|
| 25 mph | 2.9 (use 3.0) | 2.7 (use 3.0) | 3.1 | 2.2 |
| 30 mph | 3.3 | 3.1 | 3.5 | 1.9 |
| 35 mph | 3.6 | 3.4 | 3.9 | 1.6 |
| 40 mph | 4.0 | 3.7 | 4.3 | 1.4 |
| 45 mph | 4.4 | 4.1 | 4.7 | 1.3 |
| 50 mph | 4.7 | 4.4 | 5.1 | 1.1 |
| 55 mph | 5.1 | 4.7 | 5.5 | 1.0 |
| 60 mph | 5.5 | 5.1 | 5.9 | 1.0 |
| 65 mph | 5.8 | 5.4 | 6.3 (over 6) | 0.9 |
Quick answer
Traffic signal timing has three parts. The yellow change interval uses the ITE kinematic formula Y = t + v ÷ (2a + 2gG): perception-reaction time t (1.0 s), approach speed v in ft/s (mph × 1.47), deceleration a (10 ft/s²) and grade G as a decimal (g = 32.2 ft/s²), rounded up to the next 0.1 s; MUTCD guidance keeps yellow between 3 and 6 seconds. The all-red clearance is R = (W + L) ÷ v, the time to cross the intersection width W plus a vehicle length L. Pedestrian clearance is the crossing distance divided by 3.5 ft/s (MUTCD), after a walk interval of at least 7 s. The cycle length then comes from Webster's formula C₀ = (1.5L + 5) ÷ (1 − Y), where L is the total lost time and Y the sum of critical flow ratios, and green time is shared in proportion to each phase's flow ratio.
Examples
| Item | Inputs | Result |
|---|---|---|
| Yellow | 30 mph, level | 3.3 s |
| Yellow | 45 mph, level | 4.4 s |
| Yellow | 45 mph, 3% downgrade | 4.7 s |
| All-red | 45 mph, W 60 ft, L 20 ft | 1.3 s |
| Pedestrian clearance | 48 ft at 3.5 ft/s | 13.7 s |
| Webster cycle | L = 12 s, Y = 0.60 | 57.5 s → 60 s |
Enter your approach speed and crossing distance above for the change intervals, and phase volumes for the cycle and splits.
Summary
This traffic signal timing calculator covers the numbers needed for a preliminary fixed-time plan. The change-interval section applies the ITE kinematic equation for the yellow change interval with grade, the all-red clearance from intersection width and vehicle length, and the MUTCD pedestrian walk and clearance times with the 3.5 ft/s walking speed and the 3 ft/s check from the push button. The cycle section applies Webster's optimal cycle formula C₀ = (1.5L + 5) ÷ (1 − Y) to the critical demand and saturation flow of each phase, splits the effective green by flow ratio, and flags phases whose green is shorter than the pedestrian time. US (mph, ft) and metric (km/h, m) units are supported.
How it works
- Enter the approach speed, grade, intersection width (stop line to far side) and vehicle length to get the yellow and all-red intervals.
- Enter the crosswalk length, walking speed (3.5 ft/s per MUTCD) and walk interval to get the pedestrian clearance and total pedestrian time.
- Optionally press "Use Y + AR as lost time" to carry the change interval into the cycle calculation.
- Choose the number of phases and enter each phase's critical-lane demand and saturation flow.
- Webster's formula Co = (1.5L + 5) / (1 − Y) gives the cycle, rounded up to 5 s, and the effective green is split by each phase's flow ratio.
- Check the phase table: any phase whose green is shorter than walk + pedestrian clearance is flagged.
Use cases
- Setting yellow and all-red intervals for a new or re-timed intersection approach.
- Checking whether an existing yellow light is long enough for the approach speed and grade.
- Working out pedestrian walk and flashing DON'T WALK times for a crosswalk.
- Preliminary cycle length and green split design with Webster's method.
- Transportation engineering coursework and PE exam practice.
- Quick checks before running signal optimisation software.