Last updated: July 31, 2026
Gradient Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
slope = (y₂−y₁)/(x₂−x₁); if x₂ = x₁, line is vertical
Where:
- x1=x₁
- y1=y₁
- x2=x₂
- y2=y₂
Worked Examples
Positive slope
Use points (1,2) and (5,10).
- 1Find rise y₂−y₁ = 8
- 2Find run x₂−x₁ = 4
- 3Divide rise by run
Negative slope
Use points (2,9) and (6,1).
- 1Rise = 1−9 = −8
- 2Run = 6−2 = 4
- 3Slope = −8/4
Vertical line
Use points with same x value.
- 1Run is zero because x₂=x₁
- 2Slope is undefined for vertical lines
- 3Calculator flags vertical case
Introduction
Gradient (slope) describes how steep a line is between two points. This calculator returns slope and whether the line is vertical.
Formula Overview
Gradient Calculator uses a deterministic math model based on the calculator logic in calculation.ts.
slope = (y₂−y₁)/(x₂−x₁); if x₂ = x₁, line is vertical
Inputs are validated before computation
Outputs are rounded consistently for readable results
Invalid values return safe fallback outputs
Input Guide
Use each input key exactly as defined below to match calculator wiring and test coverage.
- 1
x1: x₁
- 2
y1: y₁
- 3
x2: x₂
- 4
y2: y₂
Output Guide
These output IDs map directly to the return object keys in calculation.ts.
- 1
slope: Rate of change (y₂−y₁)/(x₂−x₁)
- 2
isVertical: True when x₂ equals x₁ and slope is undefined
Validation Rules
The calculator checks for finite numeric values and applies domain constraints before solving.
Required fields must be present
Domain limits are enforced (for example positive lengths or valid operators)
Invalid or non-finite entries resolve to safe defaults
Use examples to verify expected behavior quickly
How to Use
Enter inputs, run calculation, and interpret the primary output first before reviewing supporting values.
Provide all required inputs
Click calculate
Read primary output first
Use secondary outputs for deeper analysis
Practical Uses
This calculator supports classroom work, engineering checks, and fast verification tasks.
Homework and exam preparation
Design and geometry validation
Spreadsheet cross-checking
Quick scenario analysis
FAQs
What does the Gradient Calculator compute?
It computes Gradient (Slope), Vertical Line Flag from validated input values.
Which inputs are required?
Required inputs are: x₁, y₁, x₂, y₂.
How are invalid values handled?
If inputs are invalid or out of domain, the calculator returns safe default outputs instead of invalid math.
Are results rounded?
Yes. Numeric values are rounded in calculation.ts (typically to six decimal places).
Can I use negative or decimal values?
Decimals are accepted where mathematically valid; sign/domain constraints are enforced by the calculator logic.
How can I verify results?
Use the worked examples and compare each output key with manual calculations or trusted references.