Elevator speed and travel time calculator

Flight time between floors for a jerk-limited (S-curve) elevator ride from travel distance, rated speed, acceleration and jerk, with whether rated speed is reached.

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Result

Flight time: 15.21 s
Top speed reached: 500 ft/min
Average speed: 394 ft/min
Trip needed to reach rated speed: 26.8 ft
Peak acceleration reached: 3.281 ft/s²
Motion profile: reaches rated speed

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. First-principles kinematics with no code limit, so no trade check is pending for this calculator. Terms of use and estimate disclaimer.

Drawing

Speed through the trip: the S-curve ramps, the cruise, and the stop.

Working

Distance needed to reach rated speed and stop again
$d_v = v\left(\dfrac{v}{a} + \dfrac{a}{j}\right)$
d_v = 2.54 × (2.54 ÷ 1 + 1 ÷ 1.5) ≈ 8.145 m
= 8.15 m (rounded up: a distance needed)
Flight time (travel at least d_v, so rated speed is reached)
$t = \dfrac{d}{v} + \dfrac{v}{a} + \dfrac{a}{j}$
t = 30.48 ÷ 2.54 + 2.54 ÷ 1 + 1 ÷ 1.5 ≈ 15.207 s
= 15.21 s
Peak acceleration actually reached on this trip
$a_p = a'$
a_p = 1 m/s², reached on this trip
= ≈ 1 m/s²
Average speed over the trip
$\bar{v} = d \div t$
30.48 ÷ 15.2066666666667 ≈ 2.004 m/s
= 2.004 m/s

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.

Notes

Flight time runs from the car starting to move until it stops level. Door opening and closing, dwell and start delay are not included.
No elevator code sets ride time. Acceleration and jerk are ride comfort settings chosen by the designer; values near 1.0 m/s² and 1.0 to 1.6 m/s³ are common for passenger cars. That range is a rule of thumb, not a code value; use the drive maker's settings for the drive you choose.

Method

The S-curve ride

A modern elevator does not jump to full acceleration. The acceleration ramps up at a set rate called jerk, holds, then ramps down as the car approaches rated speed, and the same happens in reverse to stop. That gives the smooth S-shaped speed curve passengers feel as a comfortable ride.

On a long trip the car reaches rated speed and cruises. Accelerating to rated speed and stopping again uses a distance of v times (v over a plus a over j). The flight time is then the travel divided by v, plus v over a, plus a over j.

Short trips

If the trip is shorter than that distance, the car never reaches rated speed. When it still reaches full acceleration, the time is a over j plus the square root of (a over j) squared plus 4d over a. On very short trips it never reaches full acceleration either, and the motion is made only of jerk phases; the time is then the cube root of 32d over j.

If the rated speed is so low that the car would reach it before reaching full acceleration, the peak acceleration is limited to the square root of v times j, and the same formulas are used with that value.

What it does not include

Door times, passenger transfer and the start delay are left out: this is flight time only. No elevator code governs ride time, so no clause is cited; the derivation is in the calculator's spec file.

Formulas

Distance to reach rated speed and stop

d_v = v (v/a + a/j)

d_v = v\left(\dfrac{v}{a} + \dfrac{a}{j}\right)

Flight time, d >= d_v

t = d/v + v/a + a/j

t = \dfrac{d}{v} + \dfrac{v}{a} + \dfrac{a}{j}

Flight time, 2a³/j² <= d < d_v

t = a/j + sqrt((a/j)^2 + 4d/a)

t = \dfrac{a}{j} + \sqrt{\left(\dfrac{a}{j}\right)^2 + \dfrac{4d}{a}}

Flight time, d < 2a³/j²

t = cbrt(32 d / j)

t = \sqrt[3]{\dfrac{32d}{j}}

Code basis: clause and edition

Standard	Edition	Clause	What it covers
First-principles kinematics (jerk-limited S-curve)	n/a	Derivation in this calculator's spec	Flight time from distance, speed, acceleration and jerk

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
Travel distance `travel`	metres (m)	0.5 to 600	30.48
Rated speed `ratedSpeed`	metres per second (m/s)	0.1 to 20	2.54
Acceleration `acceleration`	metres per second squared (m/s²)	0.1 to 2	1
Jerk `jerk`	metres per second cubed (m/s³)	0.1 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)
30 m at 2.5 m/s, 1.0 m/s², 1.5 m/s³ (reaches rated speed)	flightTime: 15.17 s, peakSpeed: 2.5 m/s, averageSpeed: 1.978 m/s, distanceToRated: 7.92 m, profile: reaches rated speed
One floor of 3.5 m at 2.5 m/s (full acceleration, rated speed not reached)	flightTime: 4.47 s, peakSpeed: 1.567 m/s, averageSpeed: 0.783 m/s, distanceToRated: 7.92 m, profile: reaches full acceleration but not rated speed
0.5 m relevel-length trip (jerk phases only)	flightTime: 2.2 s, peakSpeed: 0.454 m/s, averageSpeed: 0.227 m/s, distanceToRated: 7.92 m, profile: too short to reach full acceleration
Slow car: 10 m at 0.5 m/s, 1.0 m/s², 1.0 m/s³ (acceleration limited by speed)	flightTime: 21.41 s, peakSpeed: 0.5 m/s, averageSpeed: 0.467 m/s, distanceToRated: 0.71 m, peakAcceleration: 0.707 m/s², profile: reaches rated speed
Short trip where jerk governs: 0.5 m at 0.5 m/s, 2 m/s², 0.1 m/s³ (peak acceleration below the cap)	flightTime: 5.43 s, peakSpeed: 0.184 m/s, averageSpeed: 0.092 m/s, distanceToRated: 2.24 m, peakAcceleration: 0.136 m/s², profile: too short to reach full acceleration

For AI agents

This calculator is also the MCP tool elevator_travel_time 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.