Perpendicular Line Through a Point Calculator

Draw perpendicular lines from any given point. Pick your line format and see working steps. Save equations as files for school, work, and sharing.

Pick the format you already have.
Enter the slope and intercept of the given line.
Vertical lines are allowed (x₁ = x₂).
Example: 2x − y + 3 = 0
Use any real numbers for coefficients.
If b = 0, the line is vertical.
Reset

Tip: For best “standard form”, use clean decimals or fractions.

Example Data Table

Given line Point Perpendicular line result
y = 2x + 3 (1, -1) y + 1 = -0.5(x - 1)
Through (0, 3) and (2, 7) (4, 0) y - 0 = -0.5(x - 4)
2x - y + 3 = 0 (0, 0) y = -0.5x + 0

Values are shown in point-slope or slope-intercept forms for clarity.

Formula Used

If a non-vertical line has slope m₁, the perpendicular slope is the negative reciprocal: m₂ = −1 / m₁.

Using the point (x₀, y₀), the perpendicular line in point-slope form is: y − y₀ = m₂(x − x₀).

Special cases: a vertical line is perpendicular to a horizontal line, and vice‑versa.

How to Use This Calculator

  1. Select how your given line is defined.
  2. Enter the point coordinates (x₀, y₀).
  3. Fill the line inputs for your chosen method.
  4. Press Calculate to view the result above.
  5. Use CSV or PDF downloads for saved outputs.

Results appear under the header and above the form.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.