Formula used
- Velocity change: a = (v₂ − v₁) / t
- Displacement: s = u·t + ½·a·t² → a = 2(s − u·t)/t²
- Scale reading: N = m(g + a) → a = (N/m) − g
- Cable tension estimate: T = m(g + a)
How to use this calculator
- Choose a method that matches your measurements.
- Enter signed values: up positive, down negative.
- Pick gravity, or enter a custom gravity value.
- Add mass to unlock force and tension results.
- Click Calculate to view acceleration and comfort notes.
- Use Download CSV or Download PDF to save results.
Example data table
| Scenario | Inputs | Acceleration (m/s²) | Notes |
|---|---|---|---|
| Start-up (smooth) | v₁=0, v₂=2.4, t=3.0 | 0.800 | Comfortable ramp for most passengers. |
| Braking to stop | v₁=2.0, v₂=0, t=2.5 | -0.800 | Negative means downward acceleration direction. |
| Short travel segment | s=4.5 m, u=0, t=3.0 | 1.000 | Common for moderate-speed lifts. |
| Scale reading indicates upward | m=700 kg, N=7700 N | 1.193 | Apparent weight above mg implies upward acceleration. |
1) What elevator acceleration represents
Acceleration is how quickly elevator speed changes, measured in m/s². Many passenger lifts peak around 0.6–1.2 m/s², while some high‑rise systems can exceed 1.6 m/s². For reference, 1.0 m/s² changes speed by 3.6 km/h each second. This calculator keeps “up” positive, so braking while moving upward usually produces a negative value.
2) Sign convention, distance, and speed data
Use signed inputs to match real motion. For example, a 3.0 m upward displacement is +3.0 m, and a 2.0 m downward displacement is −2.0 m. Likewise, 2.5 m/s upward speed is positive. This makes results consistent across all three calculation methods.
3) Method A: velocity change over time
When you know initial and final speed, the calculator uses a = (v₂ − v₁)/t. If v₁ = 0 and v₂ = 2.4 m/s over 3.0 s, then a = 0.8 m/s². If the lift slows from 2.0 m/s to 0 in 2.5 s, a = −0.8 m/s².
4) Method B: displacement with time
If you recorded travel distance and time, the calculator rearranges s = u·t + ½·a·t² into a = 2(s − u·t)/t². With s = 4.5 m, u = 0, and t = 3.0 s, you get a = 1.0 m/s². This is useful for short start‑up segments.
5) Method C: scale reading and apparent weight
A bathroom scale or load cell gives the normal force N, often called apparent weight. Using N = m(g + a), the calculator finds a = (N/m) − g. Example: m = 700 kg and N = 7700 N yields a ≈ 1.19 m/s² upward. If N drops below m·g, acceleration is downward.
6) Comfort, jerk, and practical limits
Passengers feel both acceleration magnitude and how fast it ramps. Many designs keep |a| near 1.0 m/s² and limit jerk with smooth control. If you enter a ramp time, the tool estimates jerk as a/ramp. For a = 1.0 m/s² and ramp = 0.8 s, jerk ≈ 1.25 m/s³.
7) Reporting and exports for documentation
Use the CSV download for spreadsheets, audits, or maintenance logs. The PDF report is handy for attaching results to inspection notes, ride‑quality checks, or commissioning documents. Include your measurement method, gravity setting, and a short note so the exported report remains clear months later.
FAQs
1) Why does my acceleration show as negative?
A negative value means the acceleration points downward with the chosen sign convention. This often happens during braking while moving upward, or when the car begins moving downward from rest. Use signed velocities and displacements for consistency.
2) Do I need to enter mass?
No. Mass is optional for the velocity and displacement methods. Add mass if you want net force, apparent weight, and cable tension estimates. The scale-reading method requires mass because it uses N = m(g + a).
3) What gravity value should I select?
Use Earth for normal elevator work. Choose a custom value if you are modeling a different gravitational environment or using a specific local convention. Gravity affects g‑force, apparent weight, and tension outputs, but not velocity-only acceleration.
4) Is “cable tension” the same as motor torque?
No. The tension shown is a simplified estimate for the car side based on m(g + a). Real systems include counterweights, sheaves, and friction losses. Use this result for quick checks, not for final traction or motor sizing.
5) What acceleration is considered comfortable?
Many passenger elevators target about 0.6–1.2 m/s² for smooth rides, with higher values feeling more “aggressive.” Comfort also depends on jerk and vibration. Use the ramp time input to gauge jerk and compare runs consistently.
6) Why do my scale readings fluctuate?
Scales and load cells respond to vibration, floor flex, and control oscillation. Take several readings and average them, or log data if possible. Ensure the scale is stable and centered. The scale method assumes the reading approximates normal force.
Notes and limitations
- This tool assumes straight-line motion along the shaft.
- Scale method treats the reading as normal force, ignoring vibration.
- Forces are estimates and do not include counterweight dynamics.
- For safety-critical work, validate with certified instrumentation.