What is Linear Interpolation?
Linear interpolation is a method for estimating a value that falls between two known data points. If you know the values at two positions, you can estimate the value at any position in between by drawing a straight line between them.
The formula is straightforward:
y = y₀ + (x − x₀) × (y₁ − y₀) / (x₁ − x₀)
Where:
- (x₀, y₀) is the first known data point
- (x₁, y₁) is the second known data point
- x is the position where you want to estimate the value
- y is the estimated result
In practice, this is the same math pilots do mentally every time they read between the lines of a performance chart — this calculator just removes the guesswork.
When Pilots Use It
Pilots interpolate constantly — often without realizing they're doing math. Any time you look up a value in a table and your input falls between two rows or columns, you're interpolating.
Common examples:
- Performance charts — takeoff distance, climb rate, and landing distance tables rarely have your exact temperature or altitude. You read between the rows.
- Weight & balance — CG envelope charts and moment tables often require interpolation between published weights.
- Cold temperature corrections — the ICAO correction table gives values at 10°C intervals. If your OAT is −25°C, you interpolate between the −20°C and −30°C rows.
- Wind components — crosswind and headwind component charts have discrete angles. Your actual wind angle usually falls between two lines.
- Fuel planning — range and endurance tables are published at specific power settings. Your planned setting may fall between two entries.
- IFR approach plates — visibility-to-RVR conversion tables and TERPS-based climb gradients sometimes require interpolation.
Step-by-Step Example
You're planning a takeoff and need the takeoff distance at a pressure altitude of 3,200 ft. The POH table gives you:
- At 3,000 ft: 1,850 ft ground roll
- At 4,000 ft: 2,100 ft ground roll
Step 1 — Identify your known points:
- (x₀, y₀) = (3000, 1850)
- (x₁, y₁) = (4000, 2100)
Step 2 — Your target x value:
- x = 3200
Step 3 — Apply the formula:
- y = 1850 + (3200 − 3000) × (2100 − 1850) / (4000 − 3000)
- y = 1850 + 200 × 250 / 1000
- y = 1850 + 50
- y = 1,900 ft
Your estimated takeoff ground roll at 3,200 ft pressure altitude is 1,900 ft.
Double Interpolation
Sometimes your lookup value falls between rows and columns — for example, your temperature is between two columns and your altitude is between two rows. This requires double interpolation:
- First pass — interpolate along one axis (e.g., between two altitudes at the lower temperature column) to get an intermediate value.
- Second pass — interpolate along the same axis at the higher temperature column.
- Third pass — interpolate between the two intermediate values along the other axis (temperature).
This calculator handles one interpolation at a time. For double interpolation, run it twice: once for each axis.
Frequently Asked Questions
- Is linear interpolation always accurate?
- Linear interpolation assumes the relationship between data points is a straight line. For most aviation tables, this is accurate enough within one table interval. Over larger gaps, the true relationship may be curved, and linear interpolation will introduce some error. Always use the two closest data points to minimize this.
- Can I extrapolate beyond the table?
- Technically the formula works for x values outside the known range, but extrapolation is unreliable and generally not recommended for aviation use. Performance data outside the published range is not validated by the manufacturer. Stay within the table limits.
- Which field should I leave blank?
- Usually y — you know both table endpoints and the x position you're looking up, and you want to find the corresponding y value. But you can leave any one of the six fields blank and the calculator will solve for it.
- What if my two known x values are the same?
- If x₀ equals x₁, the line is vertical and interpolation is undefined — there is no unique y value for a given x. The calculator will show an error in this case.
- Does this work for non-aviation tables too?
- Absolutely. Linear interpolation is universal math. It works for any two-column table where you need to estimate a value between known entries — engineering, science, finance, or anything else.