Which formula correctly calculates slope percent?

Which formula correctly calculates slope percent?

• A. Rise ÷ Run × 100
• B. Run ÷ Rise × 100
• C. Rise × Run × 100
• D. (Rise + Run) ÷ 2 × 100

Answer: (A)

Calculating slope percent involves expressing how steep something is as a percent by comparing vertical change to horizontal distance. The standard formula is rise divided by run, then multiplied by 100 to convert to a percentage. This gives a unitless percentage that represents the grade. This form is correct because it directly measures how much you rise per unit of horizontal distance, which is exactly what percent slope (grade) is. If you rise 5 units over a run of 20 units, the slope percent is (5/20) × 100 = 25%. The other forms don’t represent slope percent correctly. Inverting the ratio (run divided by rise) would give the reciprocal of the slope, not the percent grade. Multiplying rise and run together multiplies two distances, which has no meaning for a percentage slope. Averaging rise and run and then multiplying by 100 blends two different quantities and also lacks geometric basis for slope.

Calculating slope percent involves expressing how steep something is as a percent by comparing vertical change to horizontal distance. The standard formula is rise divided by run, then multiplied by 100 to convert to a percentage. This gives a unitless percentage that represents the grade.

This form is correct because it directly measures how much you rise per unit of horizontal distance, which is exactly what percent slope (grade) is. If you rise 5 units over a run of 20 units, the slope percent is (5/20) × 100 = 25%.

The other forms don’t represent slope percent correctly. Inverting the ratio (run divided by rise) would give the reciprocal of the slope, not the percent grade. Multiplying rise and run together multiplies two distances, which has no meaning for a percentage slope. Averaging rise and run and then multiplying by 100 blends two different quantities and also lacks geometric basis for slope.