The right triangle is the most useful shape in carpentry — every roof pitch, every stair stringer, every diagonal brace, every miter cut, every square-up check is a right triangle dressed up in different language. Get comfortable with the three-side three-angle relationships and most of the math on a job site evaporates. The Chippy Tools triangle calculator does the trig and Pythagoras for you in metric or imperial — punch in any two values and the app returns the missing sides, angles, area, and perimeter.
What the triangle calculator does
The Chippy Tools triangle calculator solves any right triangle from two known values. Inputs can be two sides, one side and one acute angle, or two angles (which determines all three angles even though the third side is then unknown until a side is supplied). Outputs include all three sides, all three angles, the area, and the perimeter. The same calculator covers the special 45-45-90 isosceles right triangle, the 30-60-90 triangle, and any general right-angled triangle in between.
The app runs locally on iOS and Android with no internet required. Switch between metric and imperial without restarting and save common triangle setups (45-45-90 corner-square check, 30-60-90 hex layout, common roof pitches as triangles) as presets if you use them often.
Right triangle anatomy
A right triangle has three sides and three angles. One angle is always 90° (the right angle); the other two are acute (less than 90°) and add to 90°. The two sides forming the right angle are called the legs (sometimes “side a” and “side b”, or opposite and adjacent depending on which angle you’re calculating from). The third side, opposite the right angle, is the hypotenuse — always the longest side.
In the diagram: (1) leg a, (2) leg b, (3) hypotenuse, (4) right angle, (5) acute angle.
The vocabulary changes slightly when you specify which angle you’re working from. For an acute angle θ, the opposite side is across from θ, the adjacent side is the leg next to θ (not the hypotenuse), and the hypotenuse stays the hypotenuse. The trig functions sine, cosine, and tangent are defined off these three sides relative to θ.
How to calculate right triangle sides
Pythagoras’ theorem gives you any side from the other two:
- hypotenuse = √(leg a² + leg b²)
- leg a = √(hypotenuse² − leg b²)
- leg b = √(hypotenuse² − leg a²)
For a worked example, a triangle with legs 3 and 4 has hypotenuse √(9 + 16) = √25 = 5. The classic 3-4-5 triangle is a perfect on-site square-up check: a wall is square if a 3-unit length along one edge plus a 4-unit length along the other meets at a 5-unit diagonal.
For an imperial example, a deck with a 6-foot rise and 8-foot run has a stringer-equivalent hypotenuse of √(36 + 64) = √100 = exactly 10 feet — another perfect Pythagorean triple. Real-world dimensions rarely produce clean integers; the Chippy Tools triangle calculator returns the exact decimal value to whatever precision you need.
How to calculate right triangle angles
The three trig functions relate one acute angle to two of the three sides:
- sin(θ) = opposite / hypotenuse
- cos(θ) = adjacent / hypotenuse
- tan(θ) = opposite / adjacent
To find an angle from two sides, use the inverse functions: arcsin, arccos, or arctan. For a 3-4-5 triangle, the angle opposite the side of length 3 is arctan(3/4) ≈ 36.87°. The angle opposite the side of length 4 is arctan(4/3) ≈ 53.13°. The two acute angles always sum to 90°: 36.87 + 53.13 = 90 ✓.
Chippy Tools returns all three angles from any two known sides automatically — no need to remember which trig function applies to which angle.
Calculate Triangles On-Site
Download Chippy Tools and use the triangle calculator on iOS or Android. Offline, fast, and accurate — no signal required to set out a roof, square a wall, or find a miter angle.
Isosceles right triangles (45-45-90)
The 45-45-90 triangle is the most common special right triangle in carpentry. Both legs are equal, both acute angles are 45°, and the hypotenuse is exactly leg × √2 ≈ 1.414 × leg. So a square room with 4-metre walls has a corner-to-corner diagonal of 4 × √2 ≈ 5.66m. The 45-45-90 also describes any 45° miter cut — the cut face forms a 45-45-90 with the board’s edge.
For general (non-right) isosceles triangles — two equal sides meeting at an apex angle that isn’t 90° — the trick is to drop a perpendicular from the apex to the base. That splits the isosceles into two mirror-image right triangles, each of which the Chippy Tools triangle calculator can solve directly.
30-60-90 triangles
The 30-60-90 has angles of 30°, 60°, and 90° and side ratios of 1 : √3 : 2. If the side opposite the 30° angle is 1 unit, the side opposite the 60° angle is √3 ≈ 1.732 units, and the hypotenuse is exactly 2 units. This triangle appears in hex layouts, hip-roof corner geometry, and any application where 60° angles dominate.
The Chippy Tools calculator doesn’t enforce the special ratios — you input any two values and it returns the third. The 1 : √3 : 2 ratio is a useful sanity check on the result, but the app handles all the irrational-number arithmetic for you.
Miter angle calculator
A miter angle is half the angle between two adjoining surfaces. For two walls meeting at a square (90°) corner, each miter cut is 45°. For non-square corners — bay windows, off-square renovation walls, hexagonal posts — the miter angle is (180° − corner angle) / 2. So a 120° corner (typical hex) takes a (180 − 120) / 2 = 30° miter on each piece.
For compound miters (crown molding, where the moulding sits at a spring angle off the wall), the math gets more complex — you need both the miter angle and a bevel angle. The Chippy Tools triangle calculator handles the simple miter case directly. For compound crown-molding miters, set up the right triangle of the moulding profile and read the angle off the apex.
Common applications: roof, stairs, decks, miters
Right triangles power most carpentry calculations:
- Roof pitch — rise over run is a right triangle; the rafter is the hypotenuse. See the Roof Pitch Calculator for the dedicated workflow.
- Stair stringers — total rise and total run form a right triangle; the stringer is the hypotenuse. See the Stair Calculator.
- Deck diagonals — squaring a deck or foundation uses Pythagoras: a 3-4-5 (or 6-8-10, 9-12-15) triple proves square. See the Check Square Calculator.
- Miter cuts — every miter is a right-triangle problem disguised as an angle problem.
- Hip rafters — the hip rafter is a right triangle whose run is the diagonal of the building’s plan-view rectangle.
- Brace cuts — diagonal braces in framing are right-triangle hypotenuses sized to fit between two studs.
The triangle calculator pairs in the same Chippy Tools app with the dedicated Roof Pitch, Stair, and Check Square calculators — start with whichever workflow fits the job and drop into the general triangle calculator for any one-off geometric problem.
Triangle Maths That Just Work
Chippy Tools handles right triangles, roof pitch, stair stringers, decking, and balustrade spacing in one app. Download once, calculate anywhere — no internet required.
Imperial and metric units
Chippy Tools accepts millimetres, centimetres, metres, feet, inches, or feet and inches in any combination. Enter one side in inches and another in metres if your inputs come from mixed sources — the app converts internally and returns sides in your preferred unit. Angles are always in degrees by default with an option to switch to radians for engineering applications.
The triangle relationships are unitless in their pure form (Pythagoras, sin/cos/tan) — they hold for any consistent unit. The Chippy Tools calculator handles unit conversion so you can mix imperial and metric inputs in the same calculation without errors.
Why use a triangle calculator on your phone
The Chippy Tools app is built for tradespeople who need calculations on-site without internet. The triangle calculator is paired with the Roof Pitch Calculator, Stair Calculator, Check Square Calculator, and Decking Calculator — calculate a hip rafter, a stair stringer, a deck diagonal, and a miter cut in one workflow without re-entering measurements.
Web triangle calculators break in basements with no signal and on remote new-build sites where 4G is patchy. The Chippy Tools calculator runs locally — the answer is on screen in under a second. Switch between sin/cos/tan modes without thinking about which one applies, and pull up the calculator straight from your home screen widget when a customer asks for a quick number during the quote.
Related calculators
- Roof Pitch Calculator — same right-triangle math focused on rafters and roof pitch
- Stair Calculator — same right-triangle math focused on stair stringers
- Check Square Calculator — Pythagoras-based diagonal check for foundations, decks, and walls
- Decking Calculator — for deck dimensions where right-triangle diagonals come into play