3D Printer Belt Tension Calculator
Enter the belt mass, free span, target tension, and measured pluck frequencies to estimate belt tension and see how far each belt is from the target.
Target pluck frequency (Hz)109.15
- Belt A tension
- 9.04 N (2.03 lbf)
- Belt B tension
- 9.04 N (2.03 lbf)
- A/B tension mismatch
- 0%
- Belt A frequency adjustment
- -0.77%
- Belt B frequency adjustment
- -0.77%
- Adjustment summary
- The two calculated belt tensions match. Belt A is above the target frequency. Belt B is above the target frequency. On a CoreXY printer, alternate small adjustments because changing one belt affects the other.
Use the same free-span length for belt A and belt B when comparing a CoreXY pair.
A tuner that locks onto a harmonic instead of the fundamental overstates tension by the square of the harmonic number.
How to use this calculator
- Choose the closest belt preset, then verify or edit the belt linear mass from the belt data sheet.
- Measure the unsupported straight span of belt between the two contact points.
- Enter the target tension in newtons, or keep the Voron-style 8.9 N starting value when that procedure applies.
- Pluck each belt, enter the fundamental frequency, and use zero for belt B on a single-belt axis.
How belt frequency becomes tension
A plucked printer belt can be approximated as a vibrating string. The calculator uses the belt's linear mass, the free vibrating span, and the measured fundamental frequency to solve for tension. The belt teeth, pulley contact, nearby hardware, and bending stiffness are real effects, but the string equation is a practical first estimate when the span is straight and measured consistently.
The measured-tension formula is:
T = 4 * mu * L^2 * f^2
- T is belt tension in newtons.
- mu is belt linear mass in kg/m, so grams per meter divided by 1000.
- L is the free span in meters, so millimeters divided by 1000.
- f is the measured fundamental frequency in hertz.
To find a target frequency from a target tension, the same relation is solved backward:
ft = sqrt(Ttarget / mu) / (2 * L)
The frequency adjustment rows show (ft - f) / f * 100. A positive value means the measured frequency is below target and needs to rise; a negative value means the measured frequency is above target and needs to fall.
What moves the result most
Free span matters a lot because tension changes with the square of span length. A frequency measured on a 150 mm span cannot be compared directly with one measured on a 120 mm span. Linear mass also matters: a wider or heavier belt needs more tension to produce the same frequency on the same span.
For paired CoreXY A/B belts, the mismatch is the absolute difference between calculated tensions divided by their mean. Matching the two calculated tensions is more meaningful than matching two readings taken on different spans, so measure both belts at the same gantry position and over the same free length.
What this calculator leaves out
This tool does not decide whether a tension is safe for your printer. Safe tension depends on the belt construction, idlers, bearings, motor shafts, frame stiffness, and the printer maker's procedure. It also does not detect whether a phone tuner captured the fundamental or a harmonic; a second harmonic doubles the reported frequency and makes calculated tension four times too high.
Worked example
Suppose a 6 mm belt has a linear mass of 8.3 g/m and the free span is 150 mm. With a target tension of 8.9 N, the target frequency is 109.15 Hz. If belt A reads 110 Hz, its calculated tension is 9.04 N, or 2.03 lbf.
If belt B also reads 110 Hz, the mismatch is 0%. Each belt is 0.77% above the calculated target frequency, so the frequency adjustment is -0.77%. On a CoreXY printer, make small alternating changes because the A and B belt paths interact.
Common questions
How do I measure a 3D printer belt's frequency?
Disable the motors, move the gantry to the position specified by the printer procedure, and pluck the straight unsupported span. Use a spectrum or tuner app and record the lowest stable peak, which should be the fundamental frequency.
What belt frequency should a CoreXY or Voron printer use?
Use the procedure for the specific printer. Voron documentation gives a 150 mm A/B-belt setup target of about 110 Hz, roughly 2 lbf, as a starting point rather than a universal limit.
Why does changing one CoreXY belt affect the other belt?
CoreXY motion uses two belts whose paths both act on the moving gantry. Changing one tension can shift gantry alignment and change the loading felt by the other belt, so paired belts are usually adjusted back and forth in small steps.
How can I tell whether a tuner detected the fundamental or a harmonic?
The fundamental is normally the lowest stable peak after the pluck. If the app jumps to about two or three times the expected frequency, it is probably reading a harmonic; using that value would overstate tension by the square of that multiple.
Can two belts have matching frequencies but different tensions?
Yes, if they were measured over different free spans or if the belts have different linear masses. Frequency only maps cleanly to tension when the span length and belt mass are the same.