Quadratic Bezier Value CalculatorFree online math calculator — instant results, no sign-up
Evaluate one coordinate of a quadratic Bezier curve.
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About the Quadratic Bezier Value Calculator
The Quadratic Bezier Value Calculator evaluates one coordinate of a quadratic Bezier curve from its start, control, and end coordinates at a chosen curve parameter. Use it separately for each axis to obtain a point on a two- or three-dimensional curve. With start coordinate 0, control coordinate 10, end coordinate 20, and curve parameter 0.5, the result is 10.
- Start coordinate
- The coordinate P0 at the beginning of the curve, default 0, expressed in the same units as the control and end coordinates.
- Control coordinate
- The coordinate P1 of the control point that influences the curve's shape, default 10, expressed in the same units as the start and end coordinates.
- End coordinate
- The coordinate P2 at the end of the curve, default 20, expressed in the same units as the start and control coordinates.
- Curve parameter
- The dimensionless parameter t, default 0.5, selects a position along the curve, conventionally from 0 at the start to 1 at the end.
Formula and method
B(t) = (1 − t)^2 P0 + 2(1 − t)t P1 + t^2 P2. With the default inputs: B(0.5) = (1 − 0.5)^2 × 0 + 2(1 − 0.5) × 0.5 × 10 + 0.5^2 × 20 = 0 + 5 + 5 = 10.
- B(t)The evaluated coordinate at parameter t, in the same units as the input coordinates.
- P0The start coordinate.
- P1The control coordinate.
- P2The end coordinate.
- tThe dimensionless curve parameter.
Compute the three weights (1 − t)^2, 2(1 − t)t, and t^2; multiply each by its corresponding coordinate; then add the contributions. At t = 0.5, the weights are 0.25, 0.5, and 0.25. Applying them to 0, 10, and 20 gives contributions of 0, 5, and 5, so the result is 10.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Start coordinate0
- Control coordinate10
- End coordinate20
- Curve parameter0.5
Results
- Result10
How to use the Quadratic Bezier Value Calculator
- 1Enter the Start coordinate; use 0 for the worked example.
- 2Enter the Control coordinate as 10 and the End coordinate as 20 for the worked example, keeping all coordinates in the same units.
- 3Set the Curve parameter to 0.5 for the worked example; normally choose a value from 0 to 1.
- 4Run the calculation to evaluate the weighted sum of the three coordinates.
- 5Read the Result row: the default inputs produce 10; repeat for other axes with the same parameter if you need a full point.
Reading your result
The Result row reports B(t), the evaluated coordinate, not a distance, slope, or full multidimensional point. The default result of 10 uses the same units as the input coordinates. At t = 0 the result equals the start coordinate, and at t = 1 it equals the end coordinate.
Limitations
This tool evaluates only one coordinate and assumes all three coordinate inputs use compatible units. The usual Bezier segment corresponds to 0 ≤ t ≤ 1; values outside that interval, if accepted, extrapolate the polynomial beyond the segment. The control point generally does not lie on the curve, and the parameter generally does not represent a fraction of distance traveled. Numerical rounding may affect displayed precision.
Common questions
Why does the default result equal the control coordinate of 10?+
At t = 0.5, the result is 0.25 × 0 + 0.5 × 10 + 0.25 × 20 = 10. This equality occurs because the default control coordinate is exactly halfway between the start and end coordinates; it is not a general rule for quadratic Bezier curves.
Does t = 0.5 always give the midpoint between the start and end coordinates?+
No. It gives B(0.5) = 0.25 P0 + 0.5 P1 + 0.25 P2, which depends on the control coordinate. It equals the endpoint midpoint when P1 = (P0 + P2)/2, as with the default inputs.
How do I calculate a complete two-dimensional Bezier point?+
Evaluate the start, control, and end x-coordinates first, then evaluate their y-coordinates using exactly the same t. Combine the two results as (B_x(t), B_y(t)).
Can the evaluated coordinate exceed all three input coordinates?+
For 0 ≤ t ≤ 1, no: the weights are nonnegative and sum to 1, so the result stays between the smallest and largest input coordinates. Outside that interval, this bound no longer applies.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.