3D Printing Calculators

FDM calibration & firmware

Input Shaper Max Acceleration

SHAPER_CALIBRATE prints a frequency and a suggested max_accel, but only for the shapers and settings it tried. This page repeats Klipper’s smoothing calculation, so you can see the accel cap for any shaper at any frequency — after tuning by hand, or after changing square_corner_velocity.

Inputs

Units
Hz

shaper_freq_x or shaper_freq_y from SHAPER_CALIBRATE, or the resonance peak of that axis if you tune by hand.

mm

Klipper uses 0.12 mm for its suggestion. A lower target keeps corners sharper and allows less accel.

mm/s

square_corner_velocity from [printer]. Klipper’s default is 5 mm/s; SHAPER_CALIBRATE uses your current value.

Klipper assumes 0.1 unless damping_ratio_x/y is set. Most printers measure 0.05–0.15.

Results

Suggested max accel
7,365mm/s²

Largest accel that keeps smoothing at or below the target. Klipper prints it rounded to 100 mm/s².

Smoothing at 5000 mm/s²
0.081mm

The “smoothing ~=” figure SHAPER_CALIBRATE prints for this shaper.

Shaper duration
15.1ms

Time from the first to the last impulse. Every move is spread over this window.

The Result is indicative and educational. It does not constitute a design, a technical opinion or medical advice and does not replace calculations or verification by a person with the appropriate qualifications and authorisations. Before purchase, installation or use in practice – in particular in electrical installations – the Result should be verified by a qualified specialist. Details: Terms of Service, point 4.

Example products

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Calculation method

Each shaper replaces a move with a short train of impulses: amplitudes A_i at times t_i, built from the frequency f and damping ratio ζ exactly as in Klipper’s shaper_defs.py. With the damped period T = 1 / (f × √(1 − ζ²)), ZV lasts 0.5 T, MZV 0.75 T, ZVD and EI 1 T, 2-hump EI 1.5 T and 3-hump EI 2 T. Spreading motion over that window rounds corners. Klipper estimates the rounding from how far the impulses sit from their weighted centre t_s: offset_180 = (a/2) × Σ A_i (t_i − t_s)² / Σ A_i for a reversal, and offset_90 = √2 × Σ over t_i ≥ t_s of A_i (scv + (a/2)(t_i − t_s))(t_i − t_s) / Σ A_i for a right-angle corner taken at square corner velocity scv. Smoothing is the larger of the two. Both grow linearly with acceleration a, so the suggested max accel is the largest a that keeps smoothing at or below the target; Klipper uses 0.12 mm and prints the result rounded to 100 mm/s². Smoothing is also shown at 5000 mm/s², the figure SHAPER_CALIBRATE reports as “smoothing ~=”. The smoothing fields convert to inches with the imperial toggle; frequency, velocity and acceleration stay in Hz, mm/s and mm/s².

Exact formula

Impulses A_i at times t_i as in Klipper shaper_defs.py; t_s = Σ A_i t_i / Σ A_i. offset_180 = (a/2) Σ A_i (t_i − t_s)² / Σ A_i. offset_90 = √2 Σ_{t_i ≥ t_s} A_i (scv + (a/2)(t_i − t_s))(t_i − t_s) / Σ A_i. smoothing = max(offset_90, offset_180); max accel = largest a with smoothing ≤ target. Limits: Reproduces Klipper’s suggestion for one known frequency. It does not measure the printer or tell you how much ringing is left.

Smoothing vs remaining vibration

Two things limit accel with a shaper. Smoothing, computed here, grows with accel and with shaper length. Remaining vibration depends on how well the shaper frequency matches the printer, and the accelerometer fit reports it. A short shaper at the right frequency gives the most accel for the least smoothing.

Square corner velocity uses up the budget

offset_90 includes scv, so a higher square_corner_velocity uses up part of the smoothing target before any acceleration is applied. It only lowers the suggestion once the 90° corner is the limiting case — at low frequencies, with long shapers or with scv around 10 mm/s — and at very low frequencies the suggested accel can reach 0.

Frequently asked questions

X and Y are different frequencies.

Run it for each axis. Klipper has one max_accel for X and Y, so use the lower suggestion; Marlin can limit axes separately with M201.

Why does EI allow less accel than ZV?

EI and the multi-hump shapers tolerate a wider band of frequencies, but they spread each move over a longer time: a full damped period for EI against half of one for ZV. A longer impulse train rounds corners more at the same acceleration, so the same smoothing budget allows a lower max accel.

My number is a little off Klipper’s.

Klipper rounds the suggestion to the nearest 100 mm/s² when it prints it, so 4455 shows as 4500. Also match the damping ratio and square corner velocity your printer uses — both change the result.

Is 0.12 mm the right target?

It is the fixed target behind Klipper’s suggestion. Lower it for crisp corners on show parts and accept less accel, or raise it for fast drafts. SHAPER_CALIBRATE’s MAX_SMOOTHING only limits which shaper frequency is chosen; it does not change this target.

Do I still need to print a ringing tower?

Yes. The accel cap only limits corner rounding. It does not see a loose belt, a second resonance or a heavy toolhead, and the ringing left over depends on how well the shaper frequency matches the printer.

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