How to use the Traffic Flow, Density and Speed Calculator
- 1. Pick the calculationBasic relation, Greenshields model, fit from data or spot speed study.
- 2. Enter your dataAny two of q, k, v; or vf and kj; or k–v pairs; or a list of spot speeds.
- 3. Get the resultsMissing value, capacity, optimum speed and density, headways and mean speeds.
Traffic stream relations
The fundamental relation is q = k × vs: flow (veh/h) = density (veh/km) × space mean speed (km/h). Time headway = 3600/q seconds and spacing = 1000/k metres.
Greenshields assumed speed falls linearly with density: v = vf(1 − k/kj). Then q = vf·k − (vf/kj)k², and the maximum flow (capacity) is qmax = vf·kj/4, at k = kj/2 and v = vf/2. From observed k–v pairs the tool fits a least-squares line to find vf and kj.
Time mean speed is the simple average of spot speeds; space mean speed is their harmonic mean. Space mean speed is always less than or equal to time mean speed.
Worked example and exam tips
Free speed 80 km/h and jam density 120 veh/km: capacity = 80 × 120/4 = 2400 veh/h at 60 veh/km and 40 km/h. Spot speeds 50, 60 and 70 km/h give time mean speed 60 km/h and space mean speed 3/(1/50 + 1/60 + 1/70) = 58.9 km/h.
- Use space mean speed, not time mean speed, in q = k·v.
- For a given flow below capacity there are two densities: one uncongested, one congested.
- Greenshields is a simple model; real roads may fit other models better.
Frequently asked questions
What is jam density?
The density at which traffic stops completely (speed is zero). Vehicles are bumper to bumper.
What is the capacity in the Greenshields model?
qmax = vf × kj / 4. It occurs at half the jam density and half the free-flow speed.
What is the difference between time and space mean speed?
Time mean speed averages the speeds of vehicles passing a point. Space mean speed averages speeds over a length of road at an instant and equals the harmonic mean of spot speeds.
Is this calculator free?
Yes. You fill a short form once to see your result, and other Uncodemy tools then open without the form. Everything is calculated in your browser and nothing you type is uploaded.