Acceleration Profile (Trapezoidal) Calculator

Work out acceleration profile (trapezoidal) instantly with clear inputs, formula shown and shareable results.

About Acceleration Profile (Trapezoidal) Calculator

Working backwards from a required move time, the area under the trapezoid must equal the distance: d = v x t x (1 - accel fraction). That gives peak velocity, and dividing by the acceleration time gives the acceleration the drive must deliver. A one-third split is the classic compromise.

Formula

Trapezoid from time

v_peak = d / (t x (1 - f)); a = v_peak / (f x t), where f is the acceleration share

Worked example

With the default values below, Acceleration Profile (Trapezoidal) Calculator returns Acceleration required of 4,444.4. Change any input above and every figure here is recalculated in your browser.

Inputs used

Move distance: 300 mm
Required move time: 0.6 s
Acceleration phase share: 25 %

Results

Acceleration required: 4,444.4 mm/s²
Peak velocity: 666.67 mm/s
Acceleration time: 0.15 s
Cruise time: 0.30 s

Step by step

1Values used
2Trapezoid from time
3Acceleration required= 4,444.4 mm/s²
4Peak velocity= 666.67 mm/s
5Acceleration time= 0.15 s
6Cruise time= 0.30 s

Assumptions and limits

The result is derived only from the 3 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

What acceleration share should I use?

One third each for accelerate, cruise and decelerate minimises peak acceleration for a given time. Shorter acceleration phases raise torque demand sharply.

Why not use the full 50%?

At 50% the profile becomes triangular with no cruise phase, giving the highest peak velocity and the greatest jerk at the midpoint.