Angle (Right Triangle] Calculator

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horizontal distance

Vertical height

Please check.

To reduce errors with the on-site design drawings, you must first determine which reference value to calculate among the angle (°], slope rate (%], and gradient ratio (X:12].
If you input the horizontal distance (Run] and vertical height (Rise] in reverse, the result will be completely different, so be sure to unify the reference point to a single one when measuring.
Even minute measurement errors in short sections can widen to several centimeters at the end of a long slope, so please use a laser level to check multiple points.
When designing the drainage slope for bathrooms or terraces, the drain opening must be set as the lowest point to prevent a reverse slope, and the floor level must be precisely adjusted according to the calculated gradient.
When ordering roof or exterior wall finishing materials, you must order based on the calculated 'hypotenuse (slope] length' rather than the horizontal area, adding a loss rate to prevent material shortages.

How about this calculator?

Angle (Right Triangle] Calculator, Complete Guide to Calculating Slope and Gradient

We assist with calculating essential on-site angles, such as roof pitch, drainage slope, and ramps. Simply input the horizontal distance and height, and we instantly calculate the angle, hypotenuse, and slope ratio. Establish accurate measurement standards without complex formulas, reduce material waste, and achieve perfect construction!

Right-angled triangle and slope calculation formulas

The terms 'slope' and 'gradient,' commonly used in the field, refer to the angles and ratios of a right triangle. This calculator produces accurate data based on the Pythagorean theorem and trigonometric functions.

1. Calculation of Hypotenuse Length (Slope Length]

Hypotenuse (c] = √(horizontal distance² + vertical height²]

Calculate the total length of the slope to be actually constructed using the Pythagorean theorem.

2. Calculation of Inclination Angle

Angle (θ] = tan⁻¹(vertical height / horizontal distance] × (180 / π]

Use the arctangent function to derive the exact angle formed by the horizontal plane and the inclined plane.

3. Calculation of Slope (%]

Slope (%] = (Vertical Height / Horizontal Distance] × 100

It is a percentage of vertical height relative to horizontal distance and is used to verify standards for drainage gradients or ramps for the disabled.

Detailed Guide to Calculator Input Items

You can select and input one of two calculation methods to suit your situation.

1. Horizontal distance + vertical height method
Used for calculating drainage slopes or determining stair step heights. Please enter the measured horizontal distance and vertical height data.
2. Angle + Horizontal Distance Method
This is used for designing roof slopes or checking wall inclinations. Please enter the design angle and the reference horizontal length.
3. Select Unit
You can calculate by selecting not only the metric units of mm, cm, and m, but also the ft and in units used at wooden house construction sites.

Legal Standards and Construction Standard Specifications

The slope of the driveway and drainage gradient must comply with legal standards. These are the standard figures most frequently referenced in practice.

Applicable target	Recommended slope (%]	Angle (°]	Remarks (Field Terms]
Disabled ramp (general]	8.3% 이하	4.76° 이하	1/12 slope (BF certification required]
Outdoor parking lot entrance	17% 이하	9.6° 이하	Based on the straight section
Bathroom/Terrace Drainage	1% ~ 2%	0.5° ~ 1.1°	Drainage slope (caution: reverse slope]
Standard roof slope	30% ~ 50%	16.7° ~ 26.5°	Variable depending on the type of roofing material

note.

Standard drainage slopes for interiors are usually based on 1/100 (1%], which means a height difference of 1 cm per 1 m distance.

Essential Checklist for Fail-Free Construction

Here are tips to reduce errors that may occur at the construction site and to order materials accurately.

Material ordering based on hypotenuse length
When ordering finishing materials (panels, tiles, etc.], please place an order by adding a loss rate of 5~10% based on the calculated hypotenuse length rather than the horizontal distance.
Using a laser level is essential
When establishing slopes for long sections, it is recommended to use a laser level rather than string to accurately measure the vertical rise difference.
Set Drainage Reference Point (Level 0]
When constructing a bathroom, the key is to position the drain at the lowest point and set the door frame side higher to prevent a reverse slope.
Unit conversion and decimal point verification
Please double-check the input units, as a 1mm error over a short distance can widen to an error of several centimeters at the end of a long slope.

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Q. What exactly does '1/12 slope' on a ramp mean?
A. This means that to go up 1m vertically, you need a horizontal distance of 12m. The gradient is approximately 8.3%, and the angle is approximately 4.76 degrees.

Q. Which is used more often in the field, angle (°] or slope (%]?
A. In civil engineering or floor drainage sites, slope (%] is preferred, while in roofing or carpentry sites, angle (°] or pitch is mainly used.

Q. Why is the hypotenuse length key to estimating?
A. This is because the actual quantity of panels or tiles required to be installed on a slope is based on the length of the hypotenuse, not the horizontal distance.