Linear Interpolator
Find a missing value that falls between two known figures — for example, the flow rate at a required set point that sits between two published capacity figures in a safety valve table. Enter the two known points, leave the value you need blank, and the tool calculates it so all three points lie on one straight line. Answers are shown to one decimal place.
Known & required points
Leave exactly one cell blank — that value is calculated. For a flow rate at a required set point, enter both known points, the required set point, and leave the flow rate blank.
Graph
How It Works
Three points are collinear when they share one straight line. Given any five of the six coordinates, the sixth is fixed by linear interpolation between the two fully-known points (x₁,y₁) and (x₂,y₂):
Solve for y by entering x; solve for x (inverse interpolation) by entering y. If the blank is inside Point 1 or Point 2, the line is defined by the other two points instead — same formula, relabelled.
Worked example — safety valve capacity
A Kingston 563/573 steam capacity table lists 1334 kg/h at a 689 kPa set point and 1451 kg/h at 758 kPa. For a required set point of 710 kPa, the flow rate falls between the two published figures:
Click Example above to load this case into the tool. The same method works for any two-column table — valve capacities at different set pressures, pump flows at different heads, or gauge readings at different temperatures.
When interpolation is valid
- •The two known points must differ in x (to solve y) or in y (to solve x). Identical coordinates make the answer ambiguous and the tool reports it.
- •Extrapolation works the same way mathematically, but values outside the known range carry more uncertainty — use with care.
- •This is straight-line (linear) interpolation. For steam tables, gas properties and other non-linear data, linear interpolation between close points is a good approximation; across wide gaps it is not.