Endpoint Calculator
Solve coordinate geometry in either direction. In “Find missing endpoint” mode, enter the midpoint and one endpoint to recover the other endpoint of the segment. In “Find midpoint” mode, enter both endpoints and the tool averages them. Every result shows the substitution steps line by line and a self-check line that recomputes the midpoint from the finished pair of endpoints. Coordinates can be integers, decimals or negatives, and there is nothing to sign up for and nothing to install.
One honest note about that self-check, because the old version of this page oversold it: the check is an algebraic identity, so it confirms the arithmetic was applied consistently to the numbers you typed. It cannot tell you that you typed the right numbers. If your known endpoint was copied wrong, the answer will be wrong and the check will still pass. Check your inputs against the question first, then let the tool do the arithmetic.
Geometry aid. Coordinates can be integers, decimals or negatives. This tool works in 2D only and takes decimal numbers, so enter a fraction such as 1/2 as 0.5.
Quick Answer
Midpoint (5, 7) and known endpoint (2, 3): the missing endpoint is (8, 11), because 2 × 5 − 2 = 8 and 2 × 7 − 3 = 11. Run in the other direction, the midpoint of (2, 3) and (8, 11) is (5, 7). Both pairs of numbers are pre-filled in the two modes above, so pressing Calculate in either mode reproduces these answers exactly.
- Quick Answer
- How to use this calculator
- The formula, derived in one line
- Worked example, checked against this exact tool
- The self-check: what it proves and what it cannot
- Negative and decimal coordinates
- Related questions this tool does not answer
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
How to use this calculator
Find missing endpoint mode is for the standard homework shape of the problem: the midpoint and one endpoint are given, the other endpoint is the unknown. Enter the midpoint coordinates in the first two fields and the known endpoint in the last two, in that order. Swapping them is the single most common mistake with this problem, and it produces a plausible looking but wrong point on the opposite side of the known endpoint.
Find midpoint mode is the forward direction: two endpoints in, their average out. It is the version you need for bisecting a segment, finding the centre of a diameter, or checking a missing endpoint answer by hand. The two modes are exact inverses, so anything one mode produces can be fed into the other to get your starting numbers back.
Validation is sequential. If a field is empty or not a number, the tool names the first missing field, for example “Enter midpoint x”, and shows no result until all four fields for the active mode are filled. Reset clears all eight fields in both modes and hides the result.
The formula, derived in one line
The midpoint averages the two endpoints: M = ((x1 + x2) / 2, (y1 + y2) / 2), which is the midpoint formula as stated in the LibreTexts precalculus text, section 1.1 on the Cartesian coordinate plane. Solve that equation for the missing endpoint and the 2 moves across: x2 = 2mx − x1 and y2 = 2my − y1. That rearrangement is the whole trick, and it is why the calculator’s steps show the doubling first: it mirrors exactly what you would write on paper.
The two directions, side by side
| Job | Formula | On the worked example |
|---|---|---|
| Missing endpoint | x2 = 2mx − x1, y2 = 2my − y1 | (2 × 5 − 2, 2 × 7 − 3) = (8, 11) |
| Midpoint | mx = (x1 + x2) / 2, my = (y1 + y2) / 2 | ((2 + 8) / 2, (3 + 11) / 2) = (5, 7) |
Worked example, checked against this exact tool
Endpoint mode first. Midpoint (5, 7), known endpoint (2, 3). Missing x = 2 × 5 − 2 = 8. Missing y = 2 × 7 − 3 = 11. Missing endpoint = (8, 11). The self-check line then averages the finished pair: midpoint of (2, 3) and (8, 11) = ((2 + 8) / 2, (3 + 11) / 2) = (5, 7), which matches the midpoint you entered. Midpoint mode returns the complement: endpoints (2, 3) and (8, 11) average to (5, 7), and its check doubles that midpoint and subtracts endpoint A to land back on endpoint B, (8, 11).
The worked example plotted: M sits exactly halfway along the segment from A to B, the same distance from each end, which is the geometric meaning of averaging the coordinates.
The self-check: what it proves and what it cannot
The check line recomputes the midpoint from the two endpoints and prints it next to a tick. Because the missing endpoint was built by rearranging the midpoint formula, that recomputation must come back to your midpoint whenever the arithmetic is carried out correctly, so the line is a genuine guard against a slipped digit or a doubled value keyed in wrong inside the calculation itself. What it cannot do is catch wrong inputs. Earlier wording on this page claimed a swapped endpoint would make the check disagree. That was wrong: swapping which point you call the midpoint changes the question, the tool faithfully answers the new question, and the check still passes. Treat the check as proof the sums were done right, and spend your own attention on the step it cannot cover, copying the given points into the right fields.
Negative and decimal coordinates
Nothing in either formula cares about sign, so the same two operations handle every quadrant. Try it in endpoint mode: midpoint (−1.5, 2.5) with known endpoint (−4, 0.5) gives x2 = 2 × −1.5 − (−4) = 1 and y2 = 2 × 2.5 − 0.5 = 4.5, so the missing endpoint is (1, 4.5). The subtraction of a negative is where hand calculations usually slip, and it is exactly the case the step display helps with, because each line shows the values as substituted. In midpoint mode, (−2.5, 1.5) and (3.5, −4.5) average to (0.5, −1.5). One limit to know: inputs are decimal numbers only. A coordinate given as a fraction, such as 7/2, must be entered as 3.5, and an answer that is a neat fraction will be shown as its decimal.
Related questions this tool does not answer
Three neighbouring questions come up constantly alongside this one, and each has its own tool. For the length of the segment once you have both endpoints, a distance calculator applies the Pythagorean theorem to the coordinate differences, and the euclidean distance calculator covers the same distance formula as its own topic. For steepness rather than position, an average slope calculator works with rise over run between points. And if you are averaging three or more points, the result is properly called a centroid, not a midpoint: a centroid calculator handles that case. Keeping the jobs separate keeps each formula visible and checkable.
What competing calculators miss
Omni Calculator’s endpoint tool is polished and graphical, but it solves the missing endpoint direction only, and its own FAQ ties itself in knots over whether an endpoint and midpoint can share coordinates. CalculatorEd likewise does one direction, with a notation switch mid-page that labels the answer point X3 in one scenario and reuses the same labels differently in the next. MidpointCalculator.org is honest about its gap: its FAQ gives the missing endpoint formula but states the calculator does not solve it directly. CalculatorSoup puts the endpoint method in the text under a midpoint tool, so the working out is manual. OnlyCalculators comes closest, with an endpoint tool that verifies its answer, but it spreads attention across 3D, distance and slope extras. This page keeps both directions of the 2D problem in one tool, prints the substitution steps for whichever direction you ran, and verifies every result on the page, while stating plainly that fractions and 3D are out of scope.
Key takeaways
- Missing endpoint: double the midpoint and subtract the known endpoint, coordinate by coordinate.
- Midpoint: average the endpoints, coordinate by coordinate. The two modes are exact inverses.
- The self-check proves the arithmetic was applied consistently. It cannot catch a mistyped input, so verify the given points before calculating.
- Negatives and decimals work unchanged. Fractions must be entered as decimals, and the tool is 2D only.
Frequently asked questions
Double each midpoint coordinate and subtract the known endpoint coordinate: x2 = 2mx − x1 and y2 = 2my − y1. For midpoint (5, 7) and known endpoint (2, 3), that gives (2 × 5 − 2, 2 × 7 − 3) = (8, 11).
Average each pair of coordinates: ((x1 + x2) / 2, (y1 + y2) / 2). The midpoint of (2, 3) and (8, 11) is ((2 + 8) / 2, (3 + 11) / 2) = (5, 7). Switch the calculator to Find midpoint mode and it does exactly this.
Yes. Both formulas work for any real numbers, in any quadrant. Midpoint (−1.5, 2.5) with known endpoint (−4, 0.5) gives the missing endpoint (1, 4.5). Enter fractions as decimals, because the fields accept decimal numbers only.
Then the missing endpoint is that same point: 2 × 3 − 3 = 3 on each coordinate. The segment has zero length and all three points coincide. It is a valid input and a degenerate segment, not an error.
It proves the arithmetic was applied consistently: the tool recomputes the midpoint from the finished pair of endpoints and shows it matches the midpoint you entered. Because the answer is built by rearranging the midpoint formula, that match is guaranteed when the sums are done right. It cannot prove you typed the right inputs, so a mistyped endpoint gives a wrong answer with a passing check.
No. Addition is commutative, so averaging A then B gives the same midpoint as averaging B then A, on both coordinates. In endpoint mode the fields are not interchangeable, because the midpoint and the known endpoint play different roles in the formula.
No, this tool covers the 2D case only. The method extends directly: with a z coordinate on every point, the missing endpoint is z2 = 2mz − z1 and the midpoint gains (z1 + z2) / 2. You can run the x and y parts here and apply the same step to z by hand.
No. An endpoint is one of the two points where a line segment stops. A vertex is a corner where two edges of a polygon or lines in a figure meet. A polygon vertex can be the endpoint of two segments at once, but the formulas on this page are about one segment and its two endpoints.
For small areas plotted on a flat grid or a flat map projection, yes, the arithmetic is the same. For real geographic coordinates over any distance, averaging latitude and longitude directly is not the true halfway point on a curved Earth, so use a geodesic midpoint tool for that job instead.
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References
- Stitz and Zeager, Precalculus, via Mathematics LibreTexts. Sets of real numbers and the Cartesian coordinate plane: the midpoint formula and its justification. Accessed October 21, 2026.
- OpenStax, Intermediate Algebra 2e, via Mathematics LibreTexts. Distance and midpoint formulas and circles: averaging the coordinates of the endpoints. Accessed October 21, 2026.
- CalculatorSoup. Midpoint calculator: worked method for finding an endpoint from a midpoint and an endpoint. Accessed October 21, 2026.