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Trip Distribution (Gravity Model) Calculator

Work out trip distribution (gravity model) instantly with clear inputs, formula shown and shareable results.

About Trip Distribution (Gravity Model) Calculator

The gravity model distributes trips from an origin in proportion to each destination's attraction weighted by a friction factor that falls with travel cost. Comparing the weighted share with the raw attraction share shows how much the impedance term shifts trips: a nearby zone captures more than its size alone would suggest.

Formula

Gravity model

Tij = Pi x (Aj Fij) / sum over all j of (Aj Fij)

Pi
Trips produced
Aj
Attraction
Fij
Friction factor

Worked example

With the default values below, Trip Distribution (Gravity Model) Calculator returns Trips distributed to the destination of 230.8. Change any input above and every figure here is recalculated in your browser.

Inputs used

Trips produced by the origin zoneminimum 1 trips
1,000 trips
Attraction of the destination zoneminimum 1
500
Total attraction of all zonesminimum 1
2,500
Friction factor for this pairminimum 0.01
1.2

Results

Trips distributed to the destination
230.8 trips
Share of trips attracted
23.077% %
Impedance weighted attraction
600.00
Share ignoring impedance
20.000% %

Step by step

  1. 1Values used
  2. 2Gravity model
  3. 3Trips distributed to the destination= 230.8 trips
  4. 4Share of trips attracted= 23.077 %
  5. 5Impedance weighted attraction= 600.00
  6. 6Share ignoring impedance= 20.000 %

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Trip Distribution (Gravity Model) figure worked out?

Tij = Pi x (Aj Fij) / sum over all j of (Aj Fij). The gravity model distributes trips from an origin in proportion to each destination's attraction weighted by a friction factor that falls with travel cost.

What form does the friction factor take?

Commonly an inverse power or negative exponential of travel time, calibrated so the modelled trip length distribution matches observed data.

What values do I need to enter?

This calculator takes 4 inputs: Trips produced by the origin zone, Attraction of the destination zone, Total attraction of all zones, Friction factor for this pair. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.

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