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Endpoint Calculator | Compute Missing Endpoint From Midpoint

Find the missing endpoint of a line segment from its midpoint and one endpoint, with the doubling formula shown, plus the length and slope. The essential tool for geometry and coordinate problems.

Last updated: June 2026 · Free · No sign-up required

Enter the midpoint M and the known endpoint A; the tool solves for the other endpoint B.

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

Midpoint MEndpoint AMissing endpoint B
(3, 4)(1, 2)(5, 6)
(0, 0)(2, −3)(−2, 3)
(−1, 5)(4, 5)(−6, 5)
(2.5, 0)(1, −2)(4, 2)

info Endpoint Calculator

Free math calculator — enter your numbers and get an instant, accurate result.

info Private by design

Everything runs locally in your browser. No uploads, no accounts, no tracking.

info Works everywhere

Fully responsive and mobile-friendly — calculate on any device, any time.

info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

GivenSolve with
Midpoint + one endpointThis tool: B = 2M − A
Two endpointsMidpoint formula: M = (A + B)/2
Endpoint + length + slopeParametrize along the direction vector
Slope undefinedSegment is vertical (x's are equal)

lightbulb Worked example

Let's say you are using the Endpoint Calculator. Finds the missing endpoint of a segment from its midpoint and known endpoint, plus the segment's length and slope. Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula B = (2xₘ − x₁, 2yₘ − y₁) — double the midpoint, subtract the known endpoint and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: B = (2xₘ − x₁, 2yₘ − y₁) — double the midpoint, subtract the known endpoint

The Endpoint Calculator is built on a well-established calculation method. It uses the formula B = (2xₘ − x₁, 2yₘ − y₁) — double the midpoint, subtract the known endpoint to turn your inputs into a reliable result. Finds the missing endpoint of a segment from its midpoint and known endpoint, plus the segment's length and slope. The steps are shown on the page so you can follow the reasoning from input to output.

  1. Enter the midpoint coordinates (xₘ, yₘ).
  2. Enter the endpoint you know, A = (x₁, y₁).
  3. Because the midpoint is the average of the endpoints, doubling it and subtracting A isolates the other endpoint.
  4. Read off B, the full segment length and the slope of the line through the points.

Worked example: midpoint (3, 4), known endpoint (1, 2) → B = (2·3 − 1, 2·4 − 2) = (5, 6); the segment AB is 5.657 units long with slope 1.

What is the Endpoint Calculator?

The Endpoint Calculator is a free, browser-based math calculator tool that helps you Finds the missing endpoint of a segment from its midpoint and known endpoint, plus the segment's length and slope.. Instead of working through the math by hand or in a spreadsheet, you enter your values and the calculator returns an accurate result instantly — while still showing the formula and the steps so you can verify the reasoning. It is designed for quick everyday use: no sign-up, no installation, and everything runs locally in your browser for complete privacy.

How to use the Endpoint Calculator

  1. Enter the required values into the input fields.
  2. Press the calculate button — the result appears immediately, updated live as you change any value.
  3. Read the step-by-step breakdown below the result to see exactly how the calculation was performed.
  4. Use the interpretation guide to understand what the result means for your situation, and try different inputs to see how they change the outcome.

How to use the Endpoint Calculator

Enter the coordinates of the midpoint and the known endpoint of a line segment, and the tool finds the missing endpoint with B = (2xₘ − x₁, 2yₘ − y₁) — double the midpoint's coordinates and subtract the known endpoint. It also returns the segment's length and slope. For a midpoint of (5, 6) and one endpoint of (3, 2), the missing endpoint is (2×5 − 3, 2×6 − 2) = (7, 10).

Interpreting your result

The formula comes directly from the midpoint definition: the midpoint is the average of the two endpoints, so the missing endpoint is twice the midpoint minus the known one. This is a common algebra and geometry problem — finding the other end of a diameter given its midpoint (the circle's center), or reconstructing a line segment from partial data. The length and slope outputs complete the geometric picture, giving you the full segment description from the same inputs. The same logic extends naturally to 3D coordinates.

Common mistakes to avoid

The most common error is swapping the coordinates — the x and y components must be handled independently: 2xₘ − x₁ for x and 2yₘ − y₁ for y. Second, forgetting the factor of 2: the midpoint is the average, so reconstruction requires doubling, not adding. Third, mixing up which point is the known endpoint. Finally, applying the formula to the midpoint of a segment that does not exist — every pair of points has a midpoint, but the endpoint calculation needs the midpoint and one endpoint to be consistent.

Tips for best results

Verify your result by averaging the two endpoints — the average must equal the midpoint you were given. For circle problems, remember the diameter's midpoint IS the center. Sketch the points when possible; a quick plot catches sign errors. When working in 3D, apply the same doubling-and-subtracting to all three coordinates. Use the length output to double-check: the distance from the missing endpoint to the midpoint must equal the distance from the known endpoint to the midpoint.

Authoritative source: Wolfram MathWorld

Frequently asked questions

How do you find the missing endpoint of a segment?
Enter the required values into the input fields and press the calculate button. The tool applies the formula B = (2xₘ − x₁, 2yₘ − y₁) — double the midpoint, subtract the known endpoint and returns the result with a short explanation of each step, so you can check the working yourself.
Why does the endpoint formula work?
The Endpoint Calculator uses the standard B = (2xₘ − x₁, 2yₘ − y₁) — double the midpoint, subtract the known endpoint. You enter your values, and the calculator applies the formula step by step, showing the working so you can verify the math and understand how the result is derived rather than trusting a black box.
Does it work with negative or decimal coordinates?
The Endpoint Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Finds the missing endpoint of a segment from its midpoint and known endpoint, plus the segment's length and slope. There is no limit on usage, and it works on any device.
What if my segment is vertical?
The formula works unchanged: for a vertical segment, the x-coordinates are equal, so 2xₘ − x₁ = x₁, and only the y-coordinates move. For a midpoint of (3, 7) and endpoint (3, 2), the missing endpoint is (3, 12). The slope output will be undefined for vertical segments, which the calculator reports correctly.
Can I find an endpoint in 3D?
Yes — extend the same doubling-and-subtracting to the z-coordinate: B = (2xₘ − x₁, 2yₘ − y₁, 2zₘ − z₁). The calculator accepts 3D coordinates and returns the missing endpoint plus the 3D segment length. This is useful for spatial geometry and graphics problems where segments span three dimensions.
What does the Endpoint Calculator do?
Finds the missing endpoint of a segment from its midpoint and known endpoint, plus the segment's length and slope. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Endpoint Calculator use?
The Endpoint Calculator applies the standard formula: B = (2xₘ − x₁, 2yₘ − y₁) — double the midpoint, subtract the known endpoint. The tool walks through each step of the calculation so you can verify the numbers yourself.
Is the Endpoint Calculator free and private?
Yes — the Endpoint Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Endpoint Calculator?
The Endpoint Calculator applies the standard formula: B = (2xₘ − x₁, 2yₘ − y₁) — double the midpoint, subtract the known endpoint. It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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