About 2D Distance
Coordinate geometry bridges algebra and geometry by assigning numerical addresses (coordinates) to points in space. This makes geometric relationships calculable using algebraic tools — including the straight-line distance between any two points, which this calculator finds using the four coordinates you enter: (x₁, y₁) for Point 1 and (x₂, y₂) for Point 2.
Core formulas
- Distance between two points: √((x₂−x₁)² + (y₂−y₁)²) in 2D; add (z₂−z₁)² under the radical for 3D
- Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2)
- Slope: (y₂−y₁)/(x₂−x₁) — undefined for vertical lines
- Line equation: y = mx + b (slope-intercept), or Ax + By + C = 0 (standard form)
Worked example with the default points
With Point 1 at (0, 0) and Point 2 at (3, 4): Δx = 3, Δy = 4, so distance = √(3² + 4²) = √25 = 5 — the well-known 3-4-5 right triangle. The midpoint is (1.5, 2), the slope is 4/3 ≈ 1.333, and the angle from the positive x-axis is about 53.13°.
Coordinate systems
Cartesian (x, y, z) coordinates are most intuitive. Polar coordinates (r, θ) are more natural for rotational problems. Cylindrical and spherical coordinates extend polar to 3D. The conversion formulas between them are used constantly in physics and engineering.
Frequently Asked Questions
What is the distance formula in 2D?
How do you find the midpoint between two points?
What does it mean if the slope is undefined?
Can this calculator be used for 3D distance?
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|---|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
| Hotel housekeeping | $2–5/night | Leave daily, not just at checkout |
| Barber / hair salon | 15–20% | On pre-discount total |
| Pizza delivery | 10–15% or $3–5 minimum | Higher in bad weather |
General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|---|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|---|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |