Rotation Distance Calculator

Rotation Distance Calculator

Calculate the linear distance traveled by a wheel or gear based on its diameter and rotations, or calibrate your 3D printer's extruder rotation distance.

3D Printer Calibration (Optional)

Results:

function calculateRotationLogic() { var diameter = parseFloat(document.getElementById('diameter').value); var rotations = parseFloat(document.getElementById('rotations').value); var currentRD = parseFloat(document.getElementById('currentDistance').value); var requested = parseFloat(document.getElementById('requestedMove').value); var actual = parseFloat(document.getElementById('actualMove').value); var resultDiv = document.getElementById('rotationResult'); var standardOutput = document.getElementById('standardOutput'); var calibrationOutput = document.getElementById('calibrationOutput'); var hasStandard = !isNaN(diameter) && !isNaN(rotations); var hasCalibration = !isNaN(currentRD) && !isNaN(requested) && !isNaN(actual); if (!hasStandard && !hasCalibration) { alert("Please enter values for at least one calculation type."); return; } resultDiv.style.display = "block"; standardOutput.innerHTML = ""; calibrationOutput.innerHTML = ""; if (hasStandard) { var circumference = Math.PI * diameter; var totalDistance = circumference * rotations; standardOutput.innerHTML = "Total Linear Distance: " + totalDistance.toFixed(3) + " mm" + "Circumference: " + circumference.toFixed(3) + " mm per rotation"; } if (hasCalibration) { if (requested === 0) { calibrationOutput.innerHTML = "Requested movement cannot be zero."; } else { var newRD = currentRD * (actual / requested); calibrationOutput.innerHTML = "New Rotation Distance: " + newRD.toFixed(5) + " (Update your config)"; } } }

Understanding Rotation Distance

Rotation distance is a fundamental concept in mechanical engineering and robotics. It represents the linear distance a system moves during a single full revolution of a motor or wheel. Whether you are building a remote-controlled car or calibrating a 3D printer, understanding this metric is vital for precision.

The Standard Formula

For a wheel or gear, the rotation distance is equal to its circumference. The mathematical formula is:

Distance = π × Diameter × Number of Rotations

Rotation Distance in 3D Printing (Klipper)

In the context of Klipper firmware for 3D printers, rotation_distance is the amount of distance (in mm) that the axis moves with one full revolution of the stepper motor. It replaces the older "steps per mm" calculation method to simplify configuration.

To calibrate your extruder or axis using the tool above:

• Measure: Mark 120mm of filament from the extruder entrance.
• Command: Tell your printer to extrude 100mm.
• Compare: Measure the remaining mark. If 25mm is left, your actual move was 95mm (120 – 25).
• Calculate: Use the calibration section of the calculator to find your new value.

Practical Examples

Application	Diameter	Distance per Rotation
Small Robot Wheel	65 mm	204.20 mm
Standard Bicycle Wheel	700 mm	2199.11 mm
GT2 20-Tooth Pulley	12.73 mm	40.00 mm

Why Accuracy Matters

If your rotation distance is off by even 1%, a 200mm part will be 2mm too long or too short. In robotics, this leads to navigation errors. In 3D printing, it causes under-extrusion or over-extrusion, affecting structural integrity and visual quality. Using this calculator ensures your hardware settings match physical reality.