3-4-5 Rule Calculator

3-4-5 Rule Calculator shows whether a corner is square from two leg marks and one diagonal pull, how far to shift a leg if it is not, and the largest triangle that your walls hold.

Squaring Corners With the 3-4-5 Rule Calculator

The 3-4-5 Rule Calculator tells you whether a layout corner is square from two leg marks and one tape pull across them. When the corner is off, it gives the actual angle and how far to move a leg, so you fix it in one pass instead of guessing.

Framers use it to square wall plates and floor decks. Form setters and deck builders use it on string lines and batter boards, and anyone laying out a shed pad, patio or tile floor can use it with a tape and a few stakes.

One Corner, a Scaled Triangle or a Full Rectangle

The What to Check menu has three jobs. One Corner checks a single 90° corner from leg A, leg B and the diagonal you pulled. Scale 3-4-5 to My Walls finds the largest 3-4-5 triangle your wall lines can hold, and Rectangle compares the two corner-to-corner diagonals of a frame.

Lengths work in feet, inches, meters, centimeters or millimeters. The Tolerance panel sets how far the diagonal may miss before the corner counts as out of square, in inches for US units or millimeters for metric, with 1/8 in as the default.

The Math Behind a 3-4-5 Rule Calculator

A triangle with legs of 3 and 4 units must have a 5-unit diagonal when the corner between the legs is 90°. The Journal of Light Construction traces this to the Pythagorean theorem, which holds for any two legs, not only 3 and 4.

$$c = \sqrt{a^{2} + b^{2}}$$

So a 6 ft by 8 ft corner needs a 10 ft diagonal, and a 10 ft by 12 ft corner needs 15 ft 7-7/16 in. The first card shows that target diagonal, the layout ratio when your legs match a 3-4-5 multiple, and the two other angles of the triangle.

A common slip is marking the two legs from different starting points. Both marks have to measure from the same corner point, or the diagonal checks a triangle that does not exist on the ground.

Turning a Missed Diagonal Into an Angle

When the diagonal you pull is not the target, the calculator solves the real corner angle with the law of cosines. Here D is the measured diagonal, and a and b are the two legs.

$$\cos\theta = \frac{a^{2} + b^{2} – D^{2}}{2ab}$$

A long diagonal means the corner is open past 90°, and a short one means it is closed under 90°. Pull 10 ft 3/8 in across a 6-8-10 layout and the corner works out to 90.36°, so the hero result reads long and not square.

The second card turns that error into a move. Swinging the far end of a leg through the angle error shifts it by the leg length times the error in radians, which is 19/32 in at the end of the 8 ft leg or 7/16 in at the end of the 6 ft leg.

Lengths must be above zero and up to 2,000 ft. The tolerance can run from just over zero to 12 in (about 305 mm), and the measured diagonal must be longer than the difference between the legs and shorter than their sum, or the three marks cannot form a triangle at all.

The sketch shows a 3-4-5 corner laid out from two string lines. Both legs are marked from the same corner stake, and the diagonal is pulled between the two marks. 3 ft 4 ft 5 ft 90° string line string line

Why Bigger Triangles Check Squarer

The third card answers how square the check can prove the corner is. A tape error equal to your tolerance t hides a small angle, and that angle shrinks as the legs get longer.

$$\Delta\theta = \frac{c \times t}{a \times b}$$

At 1/8 in tolerance, a plain 3-4-5 ft triangle only proves the corner to within ±0.25°. That is enough to let a wall drift about 1/2 in over 10 ft, while a 30-40-50 ft triangle at the same tolerance narrows it to ±0.025°.

This is why JLC advises using the largest multiple your walls allow, and why one Fine Homebuilding contributor called the 3-4-5 method “extremely touchy.” The card also shows the gain from doubling the sides, which halves the angle the tape can hide.

Checking a Rectangle With Two Diagonals

Rectangle mode takes the width, the length and both corner-to-corner pulls. Each diagonal should match the target from the Pythagorean theorem, and the first card shows whether each one reads over, under or on target.

When the frame racks into a parallelogram, one diagonal grows and the other shrinks. The difference in their squares gives the corner angles and how far to slide the far long side, where L is that side’s length.

$$s = \frac{D_{1}^{2} – D_{2}^{2}}{4L}$$

A 12 ft by 16 ft deck frame should read 20 ft on both diagonals. If one reads 20 ft 1/4 in and the other 19 ft 11-3/4 in, the corners are 0.12° off and the far 16 ft side needs to slide 5/16 in toward the short diagonal’s corner.

The fourth card in this mode sizes the largest 3-4-5 triangle that fits inside the frame. Square one corner with it first, then use the diagonals as the final check.

Sizing the Triangle to Your Walls and Tying a String Loop

Scale mode takes how far each wall line runs from the corner. It finds the biggest 3-4-5 multiple in whole feet, or whole inches on short walls and 10 cm steps in metric, so walls of 14 ft and 20 ft give a 12-16-20 ft triangle with a 20 ft diagonal.

The cards show the spare length left on each wall, the next size up and its precision, and a string loop for working without a second tape. For 12-16-20 ft, tie a 48 ft loop, pin it at 0, 12 ft and 28 ft from the corner, and pull it tight.

The multiples chart lists 3-4-5 through 30-40-50 ft at your tolerance, with each size’s diagonal, precision and loop length. Once the corners are set, the Construction Elevation Calculator carries the layout into heights, and the Slope Calculator handles the same right-triangle math for rise and run.

Layout Mistakes Equal Diagonals Will Not Catch

Equal diagonals only prove square when opposite sides are already equal. A Fine Homebuilding thread describes a frame with three sides at 22 ft and one at 22 ft 2 in that measured equal diagonals but came out as a trapezoid, so check side lengths first.

String lines that are not level make every diagonal read long. Keep the lines level, or at a set slope, before pulling any tape across them.

Hooking a tape into an inside corner is harder than it sounds. As one Sawmill Creek woodworker put it, the principle is exact but our measuring tools struggle to reach the true corner, so measure to marks set out from the corner when you can.

What People Ask About the 3-4-5 Method

How do you calculate the 3-4-5 method?

Measure 3 units along one line and 4 units along the other, both from the same corner. Then measure between the two marks, and if it reads exactly 5 units, the corner is square.

Any unit works as long as all three match, so 6-8-10 ft and 900-1200-1500 mm are the same check. If the diagonal is long, the corner is open, and if it is short, the corner is closed.

Is a 3-4-5 triangle a 30-60-90 triangle?

No. Besides its right angle, a 3-4-5 triangle has angles of 36.87° and 53.13°, and the first card shows those two angles for whatever legs you enter.

A 30-60-90 triangle has sides in the ratio 1 to the square root of 3 to 2, so its sides are never all whole numbers. That is why builders use 3-4-5 for layout instead.

Is the 3-4-5 method accurate?

The geometry is exact, so the result is only as good as the tape and the marks. Carpenters on Sawmill Creek have said they would be happy with 1/16 in on a foundation diagonal and closer still on cabinets.

A small triangle magnifies tape error across a long wall. Use the largest multiple that fits, then confirm the whole layout with two matching diagonals.

How do I find the diagonal for legs that are not 3 and 4?

Square each leg, add them and take the square root. A 10 ft by 12 ft corner needs a diagonal of 15 ft 7-7/16 in, and the 3-4-5 Rule Calculator gives the result in tape-ready feet and inches.

Odd legs are common when a corner sits against an existing wall or property line. Any pair works for squaring, though a 3-4-5 multiple is easier to remember on site.