Learn: Traffic flow relationship
Traffic flow rate counts vehicles passing a point per hour. Density describes how many vehicles occupy a kilometre, and space-mean speed links these spatial and time-based descriptions.
What the formula is saying
Multiply density k by space-mean speed v: q = kv. Vehicles per kilometre multiplied by kilometres per hour gives vehicles per hour.
Read the symbols in plain language
- k
- Density
Density. Use density for the same lane set and traffic state as the supplied space-mean speed.
veh/kmUse veh/km as the base unit shown here. Use k in veh/km and speed in km/h; q is veh/h. Density and speed must represent the same lane set, road section, direction and averaging conditions. This speed is intentionally not in m/s unless converted.
- v
- Mean speed
For q = kv, use the space-mean speed of the same traffic stream and observation conditions, not a simple spot-speed arithmetic average.
km/hUse km/h as the base unit shown here. Use k in veh/km and speed in km/h; q is veh/h. Density and speed must represent the same lane set, road section, direction and averaging conditions. This speed is intentionally not in m/s unless converted.
- q
- Result to find
Traffic flow relationship. Multiplying by kilometres traveled per hour cancels distance and leaves vehicles per hour.
veh/h
Sort out the units first
Use k in veh/km and speed in km/h; q is veh/h. Density and speed must represent the same lane set, road section, direction and averaging conditions. This speed is intentionally not in m/s unless converted.
Assumptions before calculating
Assume compatible aggregate traffic measurements or a homogeneous traffic-stream state. Use space-mean speed, rather than an arbitrary arithmetic mean of spot speeds, for the stated flow-density identity.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find q and explain the result in the stated output unit.
- k · Density
- 30 veh/km
- v · Mean speed
- 80 km/h
Identify vehicles occupying each kilometre
Use density for the same lane set and traffic state as the supplied space-mean speed.
(30) = 30 veh/kmConvert spatial density into hourly flow
Multiplying by kilometres traveled per hour cancels distance and leaves vehicles per hour.
(30) × (80) = 2400 veh/h
Does this worked answer make sense?
The kilometre units cancel to leave veh/h. At a fixed compatible speed, twice the density gives twice the modeled flow; in real traffic the speed may change, so this is not a capacity prediction.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- k · Density
- 40 veh/km
- v · Mean speed
- 50 km/h
Identify vehicles occupying each kilometre
Use density for the same lane set and traffic state as the supplied space-mean speed.
(40) = 40 veh/kmConvert spatial density into hourly flow
Multiplying by kilometres traveled per hour cancels distance and leaves vehicles per hour.
(40) × (50) = 2000 veh/h
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- k · Density
- 25 veh/km
- v · Mean speed
- 72 km/h
Find: Learn: Traffic flow relationship
A hint, not the answer
Multiply density k by space-mean speed v: q = kv. Vehicles per kilometre multiplied by kilometres per hour gives vehicles per hour.
Use k in veh/km and speed in km/h; q is veh/h. Density and speed must represent the same lane set, road section, direction and averaging conditions. This speed is intentionally not in m/s unless converted.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Identify vehicles occupying each kilometre
Use density for the same lane set and traffic state as the supplied space-mean speed.
(25) = 25 veh/kmConvert spatial density into hourly flow
Multiplying by kilometres traveled per hour cancels distance and leaves vehicles per hour.
(25) × (72) = 1800 veh/h
Avoid the common trap
Do not multiply per-lane density by total multi-lane speed data with inconsistent aggregation. Do not use a free-flow speed when the supplied density describes a different congested state.
When this method applies — and when it does not
The equation is a relationship between a traffic state’s quantities, not a model predicting how speed changes with density. It does not determine road capacity, congestion onset or a safe following distance by itself.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
One idea understood. Keep going.
This optional checkmark is saved only in this browser. It is your own progress note, not a certificate.
Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Traffic flow relationship. Consistent traffic density, flow and space-mean speed; headway follows from vehicles per unit time and is not the clear following gap.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.