Slope measures how steeply a line rises or falls: m = (y₂ − y₁) / (x₂ − x₁), the change in y per unit change in x. The Toolenza calculator returns slope from two points, the corresponding angle in degrees, and the line's full equation (y = mx + b).

The same idea, different names

• Algebra — slope, gradient.
• Geometry — gradient, rate of change.
• Calculus — derivative (limit of slope as the points get closer).
• Statistics — regression coefficient (slope of the best-fit line).
• Construction — pitch, grade, fall, rake.
• Surveying — gradient in percent or per-mille (1% = 1 m rise per 100 m run).

All are computed the same way; the language depends on the field.

Slope interpretations by sign and magnitude

• m = 0 — horizontal line; no change.
• m = 1 — 45° rise (1 unit up per 1 unit right).
• m = ∞ (undefined) — vertical line; division by zero in the formula.
• m < 0 — line falls left-to-right.
• |m| > 1 — steep; |m| < 1 — gradual.

Practical conversions

• Slope to angle — θ = atan(m). Slope 0.5 = 26.6°; slope 1 = 45°; slope 2 = 63.4°.
• Slope to percentage grade — m × 100. A 5% grade is m = 0.05.
• Slope to rise:run — express as ratio. 6:12 roof pitch = slope 0.5 = 26.6°.

Pitfalls

Vertical lines have undefined slope, not infinite — division by zero isn't a number. Slope depends on scale — if the y-axis is in dollars and x is in years, slope is dollars per year; check units before quoting.