CastorPrep

Interpolation calculator

Linear and double interpolation between table rows, with every step shown.

Free, right in your browser. Every result shows its work.

Result

y at x
12.826
Fraction of the interval
0.5
  1. 1.fraction = (x − x₁)/(x₂ − x₁) = (205 − 200)/(210 − 200) = 0.5
  2. 2.y = y₁ + fraction × (y₂ − y₁) = 11.529 + 0.5 × (14.123 − 11.529)
  3. 3.y = 12.826

How it's tested on the exam

Shows up on: PE Mechanical · PE Civil · PE Electrical: Power · FE

  • Interpolating the wrong pair of rows. Bracket the value you're looking for first — a value outside the two rows is extrapolation, and tables are not linear forever.
  • Double interpolation done in one step. With two unknown coordinates (say, superheated steam at a pressure and a temperature that are both between rows), interpolate along one variable on both rows first, then between those two results.
  • Linear interpolation on a strongly curved property. Saturation pressure against temperature bends; between widely spaced rows a straight line can be off in the third significant figure. Use the closest rows the table offers.
  • Carrying too few digits. Round only at the end — rounding each intermediate value to three figures can move the final answer out of the right choice's range.

Worked example

A table gives y = 11.529 at x = 200 and y = 14.123 at x = 210. Find y at x = 205.

  1. 1.Fraction of the way from x₁ to x₂: (205 − 200) / (210 − 200) = 0.5
  2. 2.y = 11.529 + 0.5 × (14.123 − 11.529) = 11.529 + 1.297

y = 12.826

Where it is in the Handbook

  • Any tabulated property (steam, refrigerant, air, interest factors) — Every NCEES Reference Handbook

Section names as printed in the current NCEES PE Reference Handbooks (Mechanical 2.1, Civil 2.2); numbering can shift between versions. On exam day you'll use your own approved calculator — here's which models NCEES allows.