Cubic Bezier Point and Length Calculator
Evaluate a cubic Bezier curve, its tangent and an approximate length from four control points.
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
Use the cubic Bernstein weights for the position and differentiate those weights for the tangent. Approximate arc length using 2000 equal parameter intervals. The diagram preserves equal coordinate scale.
B(t)=(1−t)³P0+3(1−t)²tP1+3(1−t)t²P2+t³P3
Worked example
For P0=(0,0), P1=(100,0), P2=(100,100), P3=(200,100), t=0.5 gives (100,50), derivative (150,150) and tangent angle 45°.
Assumptions and input details
Coordinates are Cartesian: positive y points up in the diagram. The parameter is not distance along the curve. A zero derivative has no tangent direction. Arc length is a polyline approximation, not an exact integral or a certified error bound; sharply changing curves may need more precise software. All four coincident points are allowed.
References: W3C: cubic Bezier path commands
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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