Calculadora de pendiente
Halla la pendiente entre dos puntos junto con la ecuación de la recta, sus intersecciones, el ángulo, la longitud, el punto medio y la pendiente perpendicular.
Cómo usar esta calculadora
- 1Enter the x and y coordinates of your first point.
- 2Enter the coordinates of the second point.
- 3Read the slope and the equation. The perpendicular slope is there for finding a line at right angles to this one.
Cómo funciona
Fórmulas de pendiente y recta
m = (y₂ − y₁) ÷ (x₂ − x₁) Pendiente-ordenada: y = mx + b Punto-pendiente: y − y₁ = m(x − x₁) Distancia: d = √((x₂−x₁)² + (y₂−y₁)²) Punto medio: ((x₁+x₂)/2, (y₁+y₂)/2) Pendiente perpendicular = −1 ÷ m
La pendiente mide la inclinación de una recta como la elevación dividida por el avance entre dos puntos. Con ella y un punto se obtiene la ecuación completa de la recta en forma pendiente-ordenada. Una pendiente positiva sube de izquierda a derecha, una negativa baja, y una recta vertical tiene pendiente indefinida porque su avance es cero.
Ejemplo resuelto
Entre los puntos (1, 2) y (3, 6): la pendiente es (6 − 2) ÷ (3 − 1) = 2, la ecuación es y = 2x + 0, y la distancia entre ambos puntos es √(2² + 4²) ≈ 4,47.
Calculadora de pendiente: la guía completa
Rise over run, and getting the order right
Slope is rise over run: the change in y divided by the change in x. The one rule that matters is consistency — subtract the coordinates in the same order in both the numerator and the denominator. Using y₂ − y₁ over x₁ − x₂ flips the sign and gives a line pointing the wrong way.
The result is a rate of change. A slope of 2 means y increases by 2 for every 1 that x increases. In an applied context that is a speed, a price per unit, or a cost per hour — which is why slope is the bridge between geometry and every linear model in science and economics.
Zero, undefined, and why they differ
A horizontal line has a slope of exactly zero: no rise, so the ratio is 0 ÷ run. A vertical line has an undefined slope: no run, so the ratio would be rise ÷ 0, which does not exist.
The distinction matters because a vertical line cannot be written as y = mx + b at all. Its equation is x = c, and it fails the function test — one x value maps to infinitely many y values. This calculator flags the vertical case rather than returning a very large number.
Parallel and perpendicular lines
Parallel lines have identical slopes — that is the definition, since equal steepness means they never converge. Perpendicular lines have slopes whose product is −1, so each is the negative reciprocal of the other: a line of slope 2 is crossed at right angles by a line of slope −½.
The exception is the horizontal-vertical pair. A slope of 0 has no reciprocal, so the perpendicular to a horizontal line is a vertical line with an undefined slope, and the −1 rule does not literally apply.
Slope as grade and angle in the real world
Road engineers express slope as a percentage grade, which is simply the slope times 100. A 6% grade rises 6 feet over 100 feet of horizontal distance — steep enough for runaway-truck ramps. Roof pitch uses rise per 12 inches of run instead, so a 6/12 pitch is a slope of 0.5.
Accessibility standards are among the strictest applications: a wheelchair ramp is generally limited to a 1:12 slope, which is 8.33% or about 4.76°. Note how different those three numbers look for the same physical steepness — the grade percentage and the angle only agree at very shallow slopes.
Preguntas frecuentes
¿Cómo se calcula la pendiente entre dos puntos?
Se divide la diferencia de las coordenadas y entre la diferencia de las coordenadas x: m = (y₂ − y₁) ÷ (x₂ − x₁). Por ejemplo, entre (1, 2) y (3, 6) la pendiente es (6 − 2) ÷ (3 − 1) = 2.
¿Qué significa una pendiente indefinida?
Aparece en una recta vertical, donde las dos coordenadas x son iguales, así que el avance es cero. Dividir entre cero no tiene valor, por lo que la pendiente no está definida. La recta se describe simplemente como x = constante.
¿Qué es la pendiente perpendicular?
Es el opuesto del inverso de la pendiente: −1 ÷ m. Dos rectas son perpendiculares cuando el producto de sus pendientes es −1. Así, una recta de pendiente 2 es perpendicular a otra de pendiente −1/2.