Elevator traffic analysis calculator: how many elevators

Up-peak round trip time, interval and 5-minute handling capacity for a group of elevators, and the number of cars needed to meet your interval and handling targets, with every step of the working shown.

Floors served above the lobby

Upper floors the group serves, not counting the main lobby. A whole number.

Floor to floor height

Average distance between the upper floors. (ft)

Building population above the lobby

People on the floors served, at peak occupancy.

Car capacity

Rated capacity in persons. A whole number.

Number of cars in the group

Cars that serve the same floors together. A whole number.

Rated speed

Contract speed of the cars. (ft/min)

Target interval

The longest average gap between cars leaving the lobby that you accept. (s)

Target handling capacity (% of population in 5 minutes)

Share of the population the group must carry up in 5 minutes, in percent.

Allowances (6)

Design loading

Average load per trip as a fraction of capacity: 0.8 means cars leave 80 percent full (estimate).

Door opening time

From the doors starting to open until they are fully open (estimate; use the door operator's figure). (s)

Door closing time

From the doors starting to close until they are locked (estimate). (s)

Passenger transfer time

Average time for one person to enter or leave the car (estimate). (s)

Acceleration

Peak acceleration, used for the one-floor flight time. (ft/s²)

Jerk

Rate of change of acceleration, used for the one-floor flight time. (ft/s³)

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Result

Cars needed for your targets: 6
Interval with your cars: 34.0 s
Handling capacity (% in 5 minutes): 9.43
Persons carried up in 5 minutes: 113
Round trip time: 135.7 s
Passengers per trip: 12.80
Expected stops per trip: 8.06
Expected highest floor: 11.54
Time lost per stop: 7.91 s
Your cars meet both targets: no

Not engineering advice; a licensed professional checks every result. Not a substitute for a licensed engineer, the manufacturer's data or the authority having jurisdiction; confirm the code edition your jurisdiction has adopted. A planning model from probability and kinematics with no code limit, so no trade check is pending; the targets and planning times are yours to set. Terms of use and estimate disclaimer.

Drawing

Elevation of the group in the up peak. Cars are spread evenly round the trip and turn back at the expected highest floor (dashed). The cars move unless your device asks for reduced motion.

Working

Passengers per trip (car capacity times the design loading)
$P = \lambda \, CC$
P = 0.8 × 16 = 12.8
= 12.8 persons
Expected number of stops above the lobby
$S = N\left[1 - \left(1 - \dfrac{1}{N}\right)^{P}\right]$
S = 12 × (1 − (1 − 1 ÷ 12)^12.8) ≈ 8.0601
= 8.06 stops
Expected highest floor reached (the reversal floor)
$H = N - \sum_{i=1}^{N-1} \left(\dfrac{i}{N}\right)^{P}$
H = 12 − Σ (i ÷ 12)^12.8 for i = 1 to 11 ≈ 11.5428
= floor 11.54
Time to pass one floor at rated speed
$t_v = \dfrac{d_f}{v}$
t_v = 3.6576 ÷ 2.54 ≈ 1.44 s
= 1.44 s
Time lost at each stop: the one-floor flight time less t_v, plus the door times
$t_s = t_f(d_f) - t_v + t_o + t_c$
t_s = 4.54930036616041 − 1.44 + 1.8 + 3 ≈ 7.9093 s
= 7.909 s
Round trip time in the up peak
$RTT = 2Ht_v + (S + 1)t_s + 2Pt_p$
RTT = 2 × 11.5428384806729 × 1.44 + (8.06007761325261 + 1) × 7.90930036616041 + 2 × 12.8 × 1.2 ≈ 135.622 s
= 135.7 s (rounded up)
Average interval between cars leaving the lobby
$INT = \dfrac{RTT}{L}$
INT = 135.622250008279 ÷ 4 ≈ 33.906 s
= 34 s (rounded up)
Handling capacity: persons carried up in 5 minutes
$HC_5 = \dfrac{300 \, P \, L}{RTT}$
HC_5 = 300 × 12.8 × 4 ÷ 135.622250008279 ≈ 113.256
= 113 persons (rounded down)
Handling capacity as a share of the building population
$\%HC = \dfrac{100 \, HC_5}{U}$
%HC = 100 × 113.255752644293 ÷ 1200 ≈ 9.438 %
= 9.43 % (rounded down)
Cars needed to meet both of your targets
$L_{\min} = \max\left(\left\lceil \dfrac{RTT}{INT^*} \right\rceil,\ \left\lceil \dfrac{\%HC^* \, U \, RTT}{100 \times 300 \, P} \right\rceil\right)$
L_min = max(⌈135.622250008279 ÷ 30⌉, ⌈12 × 1200 × 135.622250008279 ÷ (100 × 300 × 12.8)⌉) = max(5, 6)
= 6 cars

Working is shown in the units each formula is written in; the result figures above follow the unit switch. A numeric input is taken to 15 significant digits before it is used (1033.2293579541322 kg is used as 1033.22935795413 kg); every echo of it shows that value, and a computed figure substituted into the working is quoted to 15 significant digits as well.

Code checks

FAIL
Interval at most your target of 30 s
Design target you set, not a code requirement. 34 s with 4 cars
FAIL
Handling capacity at least your target of 12 % of the population in 5 minutes
Design target you set, not a code requirement. 9.43 % with 4 cars

Notes

This is the classic up-peak model: every passenger boards at the main lobby, every floor above is equally populated, and each car leaves with the same load. Real buildings with lunch peaks, two-way traffic or uneven floors need a simulation.
Targets vary by building type and client. Office designs have long used around 12 to 15 percent in 5 minutes with an interval of 20 to 30 seconds; some current guidance accepts less. The defaults here are a starting point (estimate), not a requirement.
The door times, the transfer time and the 80 percent design loading are typical planning values (estimate). Replace them with the door operator's figures and your own loading assumption.

Method

The morning up peak

Lift planners size a group of elevators for the busiest regular moment in an office: the morning arrival, when almost everyone boards at the main lobby and rides up. If the group copes with that, it usually copes with the rest of the day.

Each car leaves the lobby with P passengers, a share of its capacity called the design loading. Each passenger picks one of the N floors above, all equally likely. The car stops at every floor someone chose, turns back at the highest one, and returns to the lobby express.

Stops and the highest floor

The chance that nobody picks a given floor is (1 − 1/N) to the power P, so the expected number of stops is S = N times one minus that. The expected highest floor is H = N minus the sum of (i/N) to the power P for i from 1 to N − 1. Both come straight from probability.

Round trip time, interval and handling capacity

The car runs up to floor H and back, 2H floors at rated speed, taking t_v = d_f / v per floor. Each of the S stops, plus the stop at the lobby, costs an extra t_s: the one-floor flight time less t_v, plus the door opening and closing times. Each passenger takes t_p to get in and again to get out. So RTT = 2H t_v + (S + 1) t_s + 2P t_p.

With L cars spread evenly, a car leaves the lobby every RTT / L seconds: the interval. In 5 minutes the group carries 300 P L / RTT people up. Dividing by the population gives the handling capacity as a percentage, the figure planners compare with a target.

Targets

No elevator code says how many elevators a building needs; the targets come from the client and from planning guidance. Office designs have long aimed for about 12 to 15 percent of the population in 5 minutes and an interval of 20 to 30 seconds, with prestige buildings at the short end. Set your own; the calculator then gives the fewest cars that meet both.

Formulas

Expected stops

S = N [1 - (1 - 1/N)^P]

S = N\left[1 - \left(1 - \dfrac{1}{N}\right)^{P}\right]

Expected highest floor

H = N - sum_{i=1}^{N-1} (i/N)^P

H = N - \sum_{i=1}^{N-1} \left(\dfrac{i}{N}\right)^{P}

Round trip time

RTT = 2 H t_v + (S + 1) t_s + 2 P t_p, with t_v = d_f / v and t_s = t_f(d_f) - t_v + t_o + t_c

RTT = 2Ht_v + (S + 1)t_s + 2Pt_p

Interval

INT = RTT / L

INT = \dfrac{RTT}{L}

Handling capacity in 5 minutes

HC_5 = 300 P L / RTT; %HC = 100 HC_5 / U

HC_5 = \dfrac{300 \, P \, L}{RTT}

Code basis: clause and edition

Standard	Edition	Clause	What it covers
Up-peak round trip time model (CIBSE Guide D, Transportation systems in buildings, section 3)	n/a	Derivation in this calculator's spec	Expected stops, highest reversal floor, round trip time, interval and handling capacity

Rules are restated in our own words and computed for your inputs; no table or text from a standard is reproduced. The adopted edition varies by jurisdiction, so confirm the one your authority having jurisdiction enforces.

Inputs

Input	Unit	Range	Default
Floors served above the lobby `floors`	count	1 to 80	12
Floor to floor height `floorHeight`	metres (m)	2.4 to 10	3.6576
Building population above the lobby `population`	count	10 to 30000	1200
Car capacity `carCapacity`	count	4 to 60	16
Number of cars in the group `cars`	count	1 to 16	4
Rated speed `ratedSpeed`	metres per second (m/s)	0.5 to 10	2.54
Target interval `targetInterval`	seconds (s)	10 to 120	30
Target handling capacity (% of population in 5 minutes) `targetHandling`		3 to 30	12
Design loading `loadFactor`		0.4 to 1	0.8
Door opening time `doorOpen`	seconds (s)	0.5 to 10	1.8
Door closing time `doorClose`	seconds (s)	0.5 to 10	3
Passenger transfer time `transfer`	seconds (s)	0.3 to 5	1.2
Acceleration `acceleration`	metres per second squared (m/s²)	0.3 to 2	1
Jerk `jerk`	metres per second cubed (m/s³)	0.3 to 5	1.5

Worked examples

Each example below is a test the calculator must pass before it ships. The expected values were worked out by a separate implementation.

Example	Expected result (each in its declared unit)
12 floors, 1200 people, four 16-person cars at 2.5 m/s	passengers: 12.8, expectedStops: 8.06, reversalFloor: 11.54, stopTime: 7.88 s, roundTripTime: 135.4 s, interval: 33.9 s, handlingCapacity: 113, handlingPercent: 9.45, carsNeeded: 6, meetsTargets: no
The same building with six cars meets both targets	roundTripTime: 135.4 s, interval: 22.6 s, handlingCapacity: 170, handlingPercent: 14.18, carsNeeded: 6, meetsTargets: yes
Small building: 4 floors, 200 people, one 8-person car at 1 m/s	passengers: 6.4, expectedStops: 3.37, reversalFloor: 3.83, stopTime: 6.47 s, roundTripTime: 68.1 s, interval: 68.1 s, handlingCapacity: 28, handlingPercent: 14.09, carsNeeded: 2, meetsTargets: no
Tall zone: 25 floors, 2500 people, 21-person cars at 4 m/s, 25 s target	passengers: 16.8, expectedStops: 12.41, reversalFloor: 24.04, stopTime: 8.52 s, roundTripTime: 202.7 s, interval: 25.4 s, handlingCapacity: 198, handlingPercent: 7.95, carsNeeded: 14, meetsTargets: no

For AI agents

This calculator is also the MCP tool elevator_traffic_analysis at https://elevatorcalc.com/api/mcp, using the same function as this page. See how to connect, the llms.txt file, or the JSON catalogue.