Steam tables list water and steam properties (specific volume v, enthalpy h, entropy s, internal energy u) at fixed steps of pressure and temperature. Your state almost never lands exactly on a listed value, so you interpolate. There are two cases:
- Single interpolation: one input falls between two table entries and the other matches exactly.
- Double interpolation: both pressure and temperature fall between table entries (superheated tables).
The table values below are typical superheated-steam values (rounded) and are used only to show the method. Always use the table your course or project specifies, because values differ slightly between editions.
Single interpolation
Problem: find the enthalpy of superheated steam at 1.0 MPa and 220 °C.
The 1.0 MPa table lists:
| T (°C) | v (m³/kg) | h (kJ/kg) |
|---|---|---|
| 200 | 0.20602 | 2828.3 |
| 250 | 0.23275 | 2943.1 |
- Fraction of the way from 200 to 250 °C: (220 − 200) / (250 − 200) = 0.4
- h = 2828.3 + 0.4 × (2943.1 − 2828.3) = 2828.3 + 0.4 × 114.8 = 2874.2 kJ/kg
The same fraction works for every property in that row. For example, v = 0.20602 + 0.4 × 0.02673 = 0.21671 m³/kg. Check it with the linear interpolation calculator.
Double interpolation
Problem: find h at 1.1 MPa and 220 °C. 1.1 MPa isn't in the table, but 1.0 and 1.2 MPa are:
| h (kJ/kg) | 200 °C | 250 °C |
|---|---|---|
| 1.0 MPa | 2828.3 | 2943.1 |
| 1.2 MPa | 2816.1 | 2935.6 |
- Interpolate in temperature at 1.0 MPa: h = 2828.3 + 0.4 × 114.8 = 2874.22
- Interpolate in temperature at 1.2 MPa: h = 2816.1 + 0.4 × 119.5 = 2863.90
- Interpolate in pressure between those two results. 1.1 MPa is halfway: h = 2874.22 + 0.5 × (2863.90 − 2874.22) = 2869.06 kJ/kg
You get the same answer if you interpolate in pressure first. Enter the four corner values into the bilinear interpolation calculator (pressure as x, temperature as y) to check.
Saturated tables: finding the state first
In saturated tables, decide which region you're in before interpolating:
- Compare your temperature (or pressure) with the saturation value. Above Tsat at that pressure, the steam is superheated, so use the superheated table.
- For a wet mixture, interpolate the saturated-liquid and saturated-vapour properties (vf, vg, hf, hfg …) to your pressure first. Then apply the quality: h = hf + x·hfg.
- To find quality from a known property, use x = (h − hf) / hfg with interpolated hf and hfg.
Finding temperature from a property (inverse interpolation)
A common exam step is to find the temperature at a given pressure and enthalpy. At 1.0 MPa, what temperature gives h = 2900 kJ/kg?
T = 200 + (2900 − 2828.3) / (2943.1 − 2828.3) × 50 = 200 + 0.6246 × 50 ≈ 231.2 °C
Use the inverse interpolation calculator for this.
Common mistakes
- Interpolating across a phase boundary. Never interpolate between a compressed-liquid and a superheated entry, because properties jump at saturation.
- Mixing up rows and columns in double interpolation. Write the four corners in a small grid like the one above before you start.
- Rounding intermediate results. Keep at least 5–6 significant figures until the end.
- Interpolating specific volume over large steps. v is strongly curved at low pressure, so linear interpolation over wide gaps can be off by a few percent. Use the closest entries available.
How accurate is linear interpolation in steam tables?
For enthalpy and entropy in the superheated region, typical errors are well under 0.1%, which is far below the precision needed for most coursework and engineering estimates. The error grows where properties curve sharply: near the critical point, near saturation, and for specific volume at low pressure. There, use smaller table steps or property software based on the IAPWS-IF97 equations.
Doing it in a spreadsheet
The free Excel interpolation template includes a 2D sheet laid out like a steam table. Paste the block of the table you need, enter pressure and temperature, and it finds the bracketing values and does the double interpolation for you.