Geometric Lines and Curves

Professional online calculators for lines, straight lines, vectors and geometric curves

Distance and Length

Distance Between Two Points
Calculate the Euclidean distance between two points in 2D and 3D space
Distance Point to Line
Calculate the shortest distance between a point and a straight line

Angle Calculations

Angle Between Two Lines
Calculate the intersection angle between two lines in the coordinate system
Angle Between Two Vectors
Calculate the angle between two vectors using the dot product

Straight Lines and Lines

Midpoint of a Line
Calculate the midpoint between two points on a straight line
y = mx + b
Line Equation
Determine the line equation from two points or slope and point

Slope Calculations

Calculate Slope
Calculate slope from height difference and horizontal distance
m
Slope of a Line
Calculate the slope of a line from two coordinate points

Curves and Arcs

Circular Arc
Calculate circular arc properties - arc length, angle and radius
Helix
Calculate helix properties - pitch, curvature, torsion, arc length
Koch Snowflake
Calculate the fractal Koch curve - snowflake with iterative construction

About Line Geometry

Line geometry forms a fundamental basis of mathematics and finds practical applications in:

  • Engineering - Structural analysis
  • Architecture - Building design
  • Navigation - Route planning
  • Graphics - Computer visualization
  • Physics - Motion analysis
  • Surveying - Land measurement
Fundamental Line Formulas
Distance Formula
d = √[(x₂-x₁)² + (y₂-y₁)²]
Slope Formula
m = (y₂-y₁)/(x₂-x₁)
Line Equation
y = mx + b
Point-Line Distance
d = |ax + by + c|/√(a² + b²)
Tip: Analytical geometry uses coordinate systems to solve geometric problems algebraically, making complex calculations more accessible.

Practical Application Examples

Engineering
  • Structural Analysis: Beam calculations
  • Road Design: Grade and alignment
  • CAD Systems: Technical drawings
Computer Graphics
  • 3D Modeling: Object positioning
  • Animation: Motion paths
  • Game Development: Collision detection
Navigation
  • GPS Systems: Route optimization
  • Aviation: Flight path planning
  • Maritime: Course calculations
Science & Research
  • Physics: Trajectory analysis
  • Astronomy: Celestial mechanics
  • Geology: Survey mapping
Quick Reference
d = √(Δx² + Δy²)
Distance
m = Δy/Δx
Slope
y = mx + b
Line Eq.
cos θ = a·b/|a||b|
Vector Angle
Related Categories
2D Geometry
Related Areas