数学
已验证计算器，公式透明
Distance Formula Calculator.
Calculates the straight-line distance between two points in a 2D plane using the Euclidean distance formula.
您的输入
工作原理
- 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)常见问题
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.
工作原理
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.
公式
此计算器背后的数学公式，供您核对结果。
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
实际应用场景
此计算在日常生活中的应用。
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.
提示与常见错误
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.
假设与限制
- Use the stated inputs and units.
- Results are estimates for planning and education.
- Check measurements and source data before making an important decision.