Statistics & data
Graph gradient, area & prediction
Find a graph gradient, signed area or interpolated value.
Your measurements
Number formats & units
Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.
Calculated locally. No account or uploads.
Result & working
ExampleThe calculator is loading. You can read the worked example below.
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Interpretation & assumptions
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Formula & example
The relationship
What the variables mean
| Symbol | Meaning |
|---|---|
| A secant/straight-segment gradient, in y units per x unit. | |
| Signed trapezoidal area, in x units × y units. | |
| Tangent | An instantaneous slope requires a tangent or a justified local approximation. |
Worked example
- Data: x y
- 0 0 1 2 2 4 3 6
- Graph operation
- Interpolate / extrapolate y
- X coordinate of interest
- 1.5
- X-axis label / unit
- x / s
- Y-axis label / unit
- y / m
Predicted y = 3
Follow the example steps
- Use the segment from (1, 2) to (2, 4).
- m = (4 − (2))/(2 − (1)) = 2.
- y(1.5) = 2 + (2) × (1.5 − (1)) = 3.
Common mistakes
Use the change in y divided by the change in x.
Incorrect approach
(1, 3), (3, 7): m = 7/3
Correct approach
m = (7 − 3)/(3 − 1) = 2
More checks before you submit
- 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.
Method notes
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.