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Right Triangle Height (Altitude) Calculator

Find the altitude from the right angle to the hypotenuse using legs, projections or geometric relations, step by step.

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Altitude to Hypotenuse Calculator

This calculator finds Altitude h using h = (a × b) / c.

Leg a

Leg b

Hypotenuse c

Enter inputs to calculate Altitude h.

Live Visualization

Altitude to Hypotenuse Diagram

Find Altitude from Different Inputs

This calculator focuses on the altitude drawn from the right angle to the hypotenuse. It is useful when you need the internal height rather than an outer side length.

Altitude Formulas and Relations

You can solve altitude from sides using h = ab/c or from projection segments using h = sqrt(pq). Both are implemented as separate modes for different input scenarios.

Which Mode To Pick: The altitude from the right angle splits the hypotenuse into two projections. If you know the legs, use the legs method; if you know the projections p and q, the altitude is the geometric mean of the two. The strict mode rejects inputs that cannot form a valid right triangle.

Where This Calculator Helps

Breaking a triangle into smaller geometric parts for analysis.
Deriving perpendicular distances in layout and surveying tasks.
Supporting area calculations that require hypotenuse-altitude form.

Input Tips for Better Results

If entering sides, verify the hypotenuse is the largest side.
If entering projections, keep p and q non-negative and geometrically valid.
Altitude in a right triangle should be less than both leg lengths.

Pro Tip: If you know p and q, also compute c = p + q to validate segment consistency.

How To Use This Calculator

Choose the tab that matches your known values before entering numbers.
Enter values in consistent units and verify that your triangle inputs are valid.
Review the calculated result, then cross-check with a related calculator when accuracy matters.
Use related pages such as Right Triangle Area Calculator and Right Triangle Projection and Segment Calculator for advanced checks.

Calculator Modes Available

Altitude to Hypotenuse: Compute altitude h from the right-angle vertex to the hypotenuse.
Altitude squared: Altitude geometric mean theorem.

Common Mistakes and Quick Fixes

Mixing units in a single calculation. Keep all values in one unit system before solving.
Choosing a mode that does not match known inputs. Start with the closest mode to your available values.
Rounding too early. Keep full precision until the final result output.
Skipping verification. Recheck using one related calculator before using results in high-stakes work.

Frequently Asked Questions

Answers to the most common right-triangle solving questions.

01 What altitude does this page compute?

It computes the altitude drawn from the right-angle vertex to the hypotenuse, often denoted h in right-triangle geometry.

02 Which inputs can I use to find altitude?

You can solve altitude using side-based relations like h = ab/c or using hypotenuse segment relations like h = √pq, depending on known values.

03 How do I know if my altitude result is reasonable?

In a valid right triangle, altitude to the hypotenuse should be smaller than both legs. If not, inputs likely need review.

04 Can altitude be used to verify area?

Yes. You can compute area with hypotenuse and altitude and compare it with area from legs for a strong consistency check.

05 What page should I use with this one for segment checks?

Use the Right Triangle Projection and Segment Calculator to validate p, q, c, and h relationships on the same triangle.

Related Altitude Calculators

Use these focused calculators if you want to find right triangle altitude using one specific method.

Right Triangle Altitude From Sides Calculator

Open Tool

Right Triangle Altitude From Projections Calculator