Statistics & data
Graph Gradient, Interpolation & Area Calculator
Paste points read from a graph. The calculator uses straight segments between points and tells you when a prediction is extrapolated.
Your measurements
Start with the example, or enter your own values. Use a dot for decimals and e for scientific notation.
Calculated locally. No account or uploads.
Result & working
ExampleThe calculator is loading. You can read the worked example below.
Step-by-step working
The formula
m = (y₂ − y₁)/(x₂ − x₁)
y(x) = y₁ + m(x − x₁)
Area ≈ Σ [(yᵢ + yᵢ₊₁)/2] (xᵢ₊₁ − xᵢ)
| Symbol | Meaning |
|---|---|
| m | A secant/straight-segment gradient, in y units per x unit. |
| Area | Signed trapezoidal area, in x units × y units. |
| Tangent | An instantaneous slope requires a tangent or a justified local approximation. |
When to use this calculator
For a tangent-gradient exercise, enter two widely separated points on the drawn tangent. For raw curved data, the segment slope is only an approximation to the local rate, not an exact derivative.
Interpolation stays inside the sampled x range. Extrapolation extends the nearest end segment and may fail if the physical relationship changes. At an interior data point, the gradient tool chooses the segment to its left.
Trapezoids give the exact area of the piecewise-linear graph, but only approximate an unknown smooth curve. Negative regions subtract: a velocity–time area is displacement, not necessarily distance travelled.
Worked example
The calculator opens with these example values. All steps below are available even with JavaScript disabled.
- Use the segment from (1, 2) to (2, 4).
- m = (4 − (2))/(2 − (1)) = 2.
- y(1.5) = 2 + (2) × (1.5 − (1)) = 3.
Predicted y = 3
Common mistakes
- Do not use y/x as the gradient unless the line passes through the origin.
- Use the axis multiplier: an axis labelled t / 10⁻³ s is not in seconds directly.
- More displayed digits do not remove uncertainty from points read off a graph.