Math calculator
Distance Formula Calculator
Distance between two points as an exact square root and decimal with steps.
Quick answer
How do you find the distance between two points?
Subtract the x-values and the y-values, square both, add them, and take the square root. For (1, 2) and (4, 6): √(3² + 4²) = √25 = 5.
d = √((x₂ − x₁)² + (y₂ − y₁)²)
⚡ Answer updates as you type · Enter = calculate · Esc = reset
- d = √((x₂ − x₁)² + (y₂ − y₁)²)
- x₂ − x₁ = 4 − (1) = 3 • y₂ − y₁ = 6 − (2) = 4
- d = √(3² + 4²) = √(9 + 16) = √25
- Simplified: √25 = 5 ≈ 5
Find the distance between two points (x₁, y₁) and (x₂, y₂) as an exact square root and a decimal, with every step.
About this Distance Formula Calculator
The Distance Formula Calculator finds how far apart two points are on a coordinate plane. It gives the exact answer as a simplified square root (like 2√5) and the decimal, and shows every step of the distance formula for algebra and geometry homework.
What you'll need
- • x₁ and y₁ of the first point
- • x₂ and y₂ of the second point
How it works
- 1. Enter the first point.
- 2. Enter the second point.
- 3. Read the exact and decimal distance.
- 4. Follow each step of the formula.
- 5. Copy or download the work.
Worked example
Distance from (−2, 1) to (2, 3) = √(4² + 2²) = √20 = 2√5 ≈ 4.4721.
Related searches
Distance Formula Calculator FAQ
What is the Distance Formula Calculator?
The Distance Formula Calculator is a free online tool that helps you distance between two points as an exact square root and decimal with steps.
How do I use the Distance Formula Calculator?
Open the Distance Formula Calculator, enter the requested values, and review the instant estimate on the page.
Is the Distance Formula Calculator free?
Yes. The Distance Formula Calculator is free to use on Fast Online Calculator and does not require an account.
Is the distance formula the Pythagorean theorem?
Yes. The horizontal and vertical gaps are the legs of a right triangle, and the distance is the hypotenuse.
Can distance be negative?
No. Squaring removes negative signs, so distance is always 0 or more.
Does the order of the points matter?
No. (x₂ − x₁)² equals (x₁ − x₂)², so you get the same answer either way.
How do I simplify the square root?
Pull out perfect squares: √20 = √(4 × 5) = 2√5.
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