Quaternion SLERP Calculator
Interpolate two rotation quaternions along the shortest unit-quaternion arc.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Normalize both inputs and use a normalized linear limit for nearly coincident orientations.
q(t)=sin((1−t)θ)q0/sinθ+sin(tθ)q1/sinθ after shortest-arc sign adjustment
Worked example
Halfway between identity and a90° z rotation gives a45° rotation.
Assumptions and input details
Quaternion order is w,x,y,z. q and−q represent one rotation. Principal output angle is0…180°; no turn-count preservation, Euler-angle path guarantee or extrapolation.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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