Algebra & Functions
Bilinear Interpolation
f(x,y) from 4 corner points
Two-dimensional table interpolation between four corner points for steam tables and reference grids.
Calculate →Line Equation
y = m · x + b
Slope, y-intercept, and distance from two points in coordinate-plane geometry.
Calculate →Linear Extrapolation
y = y₂ + (x − x₂)(y₂ − y₁) / (x₂ − x₁)
Extrapolate a value past two known points along the same linear trend.
Calculate →Linear Interpolation
y = y₁ + (x − x₁)(y₂ − y₁) / (x₂ − x₁)
Interpolate a value between two known data points along a straight line — lerp.
Calculate →Linear Regression
y = a + b · x (least-squares)
Best-fit line through a scatter of data points by least-squares regression.
Calculate →Logarithm
log_b(y) = x ⇔ y = b^x
Logarithm of any base and its exponential inverse.
Calculate →Natural Log Equation
ln(y) = x ⇔ y = e^x
Natural logarithm (base e) and its inverse — used in growth, decay, and integration.
Calculate →Quadratic Equation
x = (−b ± √(b² − 4ac)) / (2a)
Roots, vertex, and discriminant of a quadratic ax² + bx + c = 0.
Solve →Slope
m = (y₂ − y₁) / (x₂ − x₁)
Slope of a line between two points in coordinate-plane geometry.
Calculate →Trigonometry Equations
sin · cos · tan · csc · sec · cot + inverses
Six trigonometric functions, their reciprocals, and inverses in degrees or radians.
Calculate →Algebra and functions calculators for interpolation (linear, bilinear, extrapolation, regression), linear equations (line equation, slope), polynomial roots (quadratic equation), exponentials (logarithm base-any, natural log), and trigonometry (six trig functions and their inverses).
Linear interpolation is the most-used calc in this category — it's used everywhere from thermodynamic table lookups to engineering interpolation between known data points.
When to use these calculators
Use Linear Interpolation to estimate a value between two known data points (steam tables, calibration curves, ASTM table interpolation). Use Bilinear Interpolation for 2D table lookups. Use Trigonometry for any sin/cos/tan/csc/sec/cot or inverse computation. Use Slope and Line Equation for coordinate-geometry homework.
All algebra calcs show the substituted formula step-by-step alongside the answer, so the derivation can be copied into homework or engineering notes.
Frequently Asked Questions
- How does linear interpolation work?
- Given two known points (x₁, y₁) and (x₂, y₂) and a target x between them, linear interpolation estimates y as y = y₁ + (x − x₁) × (y₂ − y₁) / (x₂ − x₁). The Linear Interpolation calculator handles both forward (find y from x) and inverse (find x from y) modes.
- What is bilinear interpolation used for?
- Bilinear interpolation handles 2D table lookups — for example, looking up a value in a steam table indexed by both temperature and pressure. It interpolates linearly in one dimension, then linearly in the second using the intermediate results. The Bilinear Interpolation calculator takes four corner points of a 2×2 grid and a target (x, y).
- What's the difference between linear interpolation and linear regression?
- Interpolation estimates a value between two known points exactly on the line connecting them. Regression fits a line through many scattered points to minimize squared error. Use Linear Interpolation when you have two reference points; use Linear Regression for a dataset with measurement scatter.