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Trajectory Time Calculator

Work out trajectory time instantly with clear inputs, formula shown and shareable results.

About Trajectory Time Calculator

A trapezoidal move accelerates, cruises, then decelerates. If the distance is shorter than twice the acceleration distance the profile is triangular and never reaches maximum velocity, so peak velocity becomes sqrt(a x d) and time is 2 sqrt(d/a).

Formula

Trapezoidal move

d_accel = v^2/(2a); if 2 d_accel >= d the profile is triangular with v_peak = sqrt(a d)

Worked example

With the default values below, Trajectory Time Calculator returns Total move time of 0.88. Change any input above and every figure here is recalculated in your browser.

Inputs used

Move distance
500 mm
Maximum velocity
800 mm/s
Acceleration
4,000 mm/s²
Settling time
0.05 s

Results

Total move time
0.88 s
Profile type
Trapezoidal - reaches cruise velocity
Peak velocity reached
800.00 mm/s
Distance used accelerating
80.00 mm

Step by step

  1. 1Values used
  2. 2Trapezoidal move
  3. 3Total move time= 0.88 s
  4. 4Profile type= Trapezoidal - reaches cruise velocity
  5. 5Peak velocity reached= 800.00 mm/s
  6. 6Distance used accelerating= 80.00 mm

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 2 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

When is a short move acceleration limited?

Whenever the distance is under v squared over a. For fast axes most short moves are triangular, which is why raising maximum velocity does nothing for them.

Why add settling time?

The axis needs time for the servo to converge inside the position window. On a compliant structure this can exceed the move time itself.

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