Mathematik
Verifizierter Rechner mit transparenter Formel
Distance Formula Calculator.
Calculates the straight-line distance between two points in a 2D plane using the Euclidean distance formula.
Ihre Eingaben
So funktioniert es
- 1
Subtract x₂ - x₁ to find the horizontal difference.
- 2
Subtract y₂ - y₁ to find the vertical difference.
- 3
Square both differences and add them together.
- 4
Take the square root of the sum to get the distance.
sqrt((x2-x1)^2 + (y2-y1)^2)Häufig gestellte Fragen
What is the distance formula?
It calculates the straight-line distance between two points (x₁,y₁) and (x₂,y₂) as √((x₂-x₁)² + (y₂-y₁)²).
Can I use this for 3D points?
No, this calculator is for 2D only. For 3D, you would add the z-difference squared under the square root.
What if the distance is negative?
Distance is always non-negative because it's a square root of a sum of squares. The result will never be negative.
Diese Rechner-Kategorie erkunden
Ergebnisse
Formel geprüftSchätzung nur zur allgemeinen Orientierung – wichtige Entscheidungen mit einem geeigneten Fachmann verifizieren.
So funktioniert es
Calculates the straight-line distance between two points in a 2D plane using the Euclidean distance formula.
- Subtract x₂ - x₁ to find the horizontal difference.
- Subtract y₂ - y₁ to find the vertical difference.
- Square both differences and add them together.
- Take the square root of the sum to get the distance.
Formeln
Die Mathematik hinter diesem Rechner, aufgeschrieben, damit Sie das Ergebnis überprüfen können.
Euclidean Distance
This formula comes from the Pythagorean theorem, treating the differences as legs of a right triangle.
Example:
Input: Points (0,0) and (3,4)
Calculation: √((3-0)² + (4-0)²) = √(9+16) = √25
Result: 5 units
Anwendungsfälle im Alltag
Wo diese Berechnung im täglichen Leben vorkommt.
Navigation
Find the shortest path between two locations on a map, ignoring roads.
Example: Distance from home to work as the crow flies.
Geometry
Determine side lengths in triangles or polygons.
Example: Check if a triangle is right-angled.
Physics
Calculate displacement between two positions.
Example: Distance traveled by an object in a straight line.
Tipps und häufige Fehler
Tips
- Double-check the order of coordinates: (x₁,y₁) is the first point, (x₂,y₂) is the second.
- Use negative numbers correctly; the formula handles them automatically.
- For quick estimates, you can approximate the square root if needed.
Common Mistakes to Avoid
- Forgetting to square the differences before adding.
- Subtracting in the wrong order (x₁ - x₂ instead of x₂ - x₁) – it doesn't matter because squaring removes the sign.
- Using the formula for 3D without adding the z-component.
Annahmen und Einschränkungen
- Use the stated inputs and units.
- Results are estimates for planning and education.
- Check measurements and source data before making an important decision.