Slope and grade calculator (%・°・‰)

Calculate slope (%/‰), angle (°), and slope distance from horizontal distance and elevation difference.

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Example preset

Choose a preset to fill the form and show results right away. Presets are examples.

Inputs

Details (back calculation/additional display)

Counting backwards

If you would like to calculate the height difference/distance from the slope, please click here (details).

Results are automatically updated on input changes (can be restored with share URL).

Results

Gradient (%)
Gradient (‰)
Angle (°)
Height difference (m)
Slope distance (m)
Gradient ratio (1:n)
Up/down per 100m (m/100m)

Schematic diagram (right triangle)

*The figure is a schematic diagram for ease of understanding (the scale will be adjusted according to the input).

Calculation formula (overview)

Show calculation formula

slope ratio: r = Δz / d

Gradient (% / ‰): grade_% = 100r, grade_‰ = 1000r

angle: θ = atan(r)

Slope distance: L = sqrt(d² + Δz²)

Display conversion table (% slope ↔ angle °)
Gradient (%) Angle (°) Per 100m (m)
0%0.00°0
5%2.86°5
10%5.71°10
15%8.53°15
20%11.31°20
30%16.70°30
50%26.57°50
100%45.00°100
*The angle is atan(勾配/100) This is a reference value calculated from.

How to use this calculator effectively

This guide helps you use Slope and grade calculator (%・°・‰) in a repeatable way: define a baseline, change one variable at a time, and interpret outputs with explicit assumptions before you share or act on results.

How it works

The page applies deterministic logic to your inputs and shows rounded output for readability. Treat it as a comparison workflow: run one baseline case, adjust a single parameter, and measure both absolute and percentage deltas. If a result seems off, verify units, time basis, and sign conventions before drawing conclusions. This approach keeps your analysis reproducible across teammates and sessions.

When to use

Use this page when you need a fast estimate, a classroom check, or a practical what-if comparison. It works best for planning and prioritization steps where you need direction and magnitude quickly before investing in deeper modeling, manual spreadsheets, or formal external review.

Common mistakes to avoid

Interpretation and worked example

Run a baseline scenario and keep that result visible. Next, modify one assumption to reflect your realistic alternative and compare direction plus size of change. If the direction matches your domain expectation and the size is plausible, your setup is usually coherent. If not, check hidden defaults, boundary conditions, and interpretation notes before deciding which scenario to adopt.

See also

Frequently asked questions

What is the difference between horizontal distance and slope distance?
The horizontal distance is the distance on the map (horizontal projection), and the slope distance is the actual length of the slope (hypotenuse).
What is the relationship between slope (%) and angle (°)?
slope ratio r=Δz/d , the angle is atan(r) It is. For example 10% is about 5.71° It is.
What is line of sight gradient?
It is the slope of the straight line connecting two points, including the observer's eye level and the object's height. Earth curvature and refraction are ignored.
Can it be used over long distances (several tens of kilometers or more)?
It can be used, but the error in plane approximation will increase. Please refer to ES-001 to calculate distance from latitude and longitude, and the horizon distance/Earth curvature head calculator (ES-014) to calculate line of sight.
What should I do first on this page?

Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.

How to use Slope and grade calculator (%・°・‰) effectively

What this calculator does

This page is for estimating outcomes by changing inputs in one controlled workflow. The model keeps your focus on variables, not output shape. Start with stable assumptions, then test sensitivity by changing one key input at a time to observe directional impact.

Input meaning and unit policy

Each input has an expected unit and a typical range. For reliable interpretation, check whether you are using the same unit system, period, and base assumptions across all runs. Unit mismatch is the most common source of unexpected drift in numeric results.

Use-case sequence

A practical sequence is: first run with defaults, then create a baseline log, then run one alternative scenario, and finally compare only the changed output metric. This sequence reduces cognitive load and prevents false pattern recognition in early experiments.

Common mistakes to avoid

Avoid changing too many variables at once, mixing incompatible data sources, and interpreting a one-time output without checking robustness. A single contradictory input can flip conclusions, so keep each experiment minimal and document assumptions as part of your note.

Interpretation guidance

Review both magnitude and direction. Direction tells you whether a strategy moves outcomes in the desired direction, while magnitude helps you judge practicality. If both agree, you can proceed; if not, rebuild the baseline and verify constraints before deciding.

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