Common Slope Mistakes

Mistake One: Inverting the Ratio

Dividing the run by the rise instead of the rise by the run. This gives the reciprocal, which for a slope of 2 returns 0.5 rather than 2. If you suspect this, check which quantity you called the rise.

Mistake Two: Percentage Grades Left as Percentages

Entering 6 for a 6 percent grade when the calculator expects the decimal slope, which is 0.06. This overstates the gradient by a factor of 100 and is the most common real world slope error.

Mistake Three: Mixed Units

Using feet for the x difference and metres for the y difference. The ratio then mixes units and has no physical meaning at all, even though the arithmetic succeeds.

Mistake Four: Expecting a Vertical Slope

Entering two points with the same x coordinate and treating the undefined result as broken. A vertical line genuinely has no slope, and is described as x equals a constant.

Mistake Five: Perpendicular as the Opposite

Taking the perpendicular slope as minus the slope rather than minus one over it. Two lines are perpendicular when the slopes multiply to minus one, which is a reciprocal relationship.

Mistake Six: Dropping the Units

Quoting a slope of 0.5 with no units on the axes. The same number describes a 50 percent gradient on a diagram in metres and a 0.05 percent gradient on a map in kilometres.