Right Triangle Altitude Calculator

Calculator

Example Data Table

Formula Used

The altitude to the hypotenuse can be found with several equivalent right triangle formulas.

• From legs: h = ab / c
• Hypotenuse: c = √(a² + b²)
• From area: h = 2K / c
• From projections: h = √(pq)
• Projection relation: p + q = c
• Leg relation: a² = cp and b² = cq

The calculator also checks h² = pq and a² + b² = c². Small nonzero values may appear because of rounding.

How to Use This Calculator

1. Select the input method that matches your known values.
2. Enter only the values required by that method.
3. Choose a unit label, such as cm, m, in, or ft.
4. Select the decimal precision for the final answer.
5. Press the calculate button.
6. Review the altitude, sides, projections, area, and checks.
7. Use CSV for spreadsheets or PDF for a printable report.

Right Triangle Altitude Guide

What the Altitude Means

A right triangle has one angle of ninety degrees. Its altitude to the hypotenuse is a special segment. It starts at the right angle and meets the hypotenuse at a square angle. This single height connects side lengths, area, and the two projected parts of the hypotenuse.

Why Similar Triangles Matter

The altitude is useful because it creates two smaller right triangles. Each smaller triangle is similar to the original triangle. That similarity gives strong formulas. You can solve the height from the legs, the hypotenuse, the area, or the projection segments. You can also check whether entered values are possible.

Using Side Lengths

When both legs are known, the method is direct. First find the hypotenuse with the square root rule. Then multiply the legs and divide by the hypotenuse. This gives the altitude because triangle area can be written in two ways. Area equals one half times leg times leg. It also equals one half times hypotenuse times altitude.

Using Projection Segments

Projection data gives another clean route. If the altitude splits the hypotenuse into parts p and q, then the height equals the square root of p times q. This relation is fast and stable. It also helps explain geometric mean problems in school geometry.

Using Area Data

Area based input is practical for design notes. If area and hypotenuse are known, the altitude equals two times area divided by hypotenuse. The calculator then estimates both legs when the values are possible. It also flags values that break triangle limits.

Precision and Units

Use consistent units for every length. If the legs are in centimeters, the altitude is also in centimeters. Area uses square centimeters. Rounding can change the last decimals, so keep more precision for teaching, drafting, or verification work.

Practical Workflow

This tool is built for exploration. Try different input modes. Compare the altitude, area, projections, and side checks. Export the result when you need a record. The CSV file is useful for spreadsheets. The PDF file is useful for notes, assignments, or shared reports.

Input Advice

For best results, start with the values you trust most. Legs usually give the strongest check. Projections are helpful when a diagram marks the hypotenuse pieces. Area and hypotenuse are useful when a drawing lists only the base and enclosed region. Always review the warning messages before exporting.

FAQs