The slope of a hill, often called its gradient or grade, measures its steepness. This measurement is fundamentally a ratio that compares the vertical change in elevation, known as the “rise,” to the corresponding horizontal distance, called the “run.” Understanding the slope is important for many activities, from civil engineering projects that require proper drainage to hiking and backcountry skiing where terrain steepness dictates safety.
Slope is commonly expressed in one of three ways: as a percentage grade, a ratio, or an angle in degrees. Percentage grade is the most frequent in road signage and construction, calculated by dividing the rise by the run and multiplying by 100. A ratio, such as 1:12, means the surface rises 1 unit for every 12 units of horizontal distance. The angular degree measurement is the actual angle of inclination from the horizontal plane, where a 45-degree slope is equivalent to a 100% grade because the rise equals the run.
The Manual Rise Over Run Method
The most fundamental way to measure slope in the field uses the classic “rise over run” principle with simple tools. This process requires establishing a measured horizontal baseline, which is the “run” component of the calculation. To begin, two stakes are driven into the ground along the direction of the slope, defining the start and end points of the measurement.
A tape measure is used to determine the horizontal distance between the two stakes, which represents the “run.” This measurement must be the horizontal distance, not the distance along the slope surface. The next step involves determining the vertical difference, or the “rise,” between the two points.
A length of string or line is stretched taut between the two stakes, and a line level is used to ensure the line is perfectly horizontal. Once the line is level, a measurement is taken from the horizontal line down to the ground at the second stake. This vertical distance is the “rise” measurement.
The final slope calculation uses the formula: (Rise / Run) x 100, which yields the percentage grade. For example, a rise of 6 feet over a run of 100 feet results in a 6 / 100 x 100 = 6% grade. This manual method is effective for short, precise measurements required for landscaping or drainage planning.
Direct Angle Measurement Using a Clinometer
A clinometer is an optical or mechanical instrument designed to measure the angle of a slope. Devices like the Abney level or an inclinometer are built on the same principle, providing a reading of the slope angle or percentage grade without needing separate rise and run measurements. Clinometers are commonly used in forestry, geology, and surveying for rapid field assessments.
To use a percent-scale clinometer, the user sights through the instrument toward a target point on the slope. For accurate slope measurement, the target must be at the same height above the ground as the user’s eye, often requiring a partner to hold a marker at that height. Keeping both eyes open when sighting helps to align the internal crosshairs with the external target.
The internal scale provides an immediate reading, usually in both degrees and percent grade. Because the measurement is taken parallel to the ground surface, it provides the angle of inclination relative to a horizontal plane. A reading of 45 degrees corresponds to a 100% slope, a relationship that is a direct function of the trigonometric tangent.
Calculating Slope with Digital Tools and Smartphone Apps
Modern technology offers simplified, though sometimes less precise, methods for measuring slope using everyday devices. Smartphone applications leverage the phone’s internal sensors to function as a digital inclinometer for quick, localized measurements. The apps use the phone’s built-in accelerometer and gyroscope to detect orientation relative to gravity.
To measure a short slope, the phone is placed directly on the surface or held upright and aligned with the slope’s direction. The app displays the inclination in degrees or percent grade in real-time, which is ideal for checking the pitch of a roof or a short ramp. While convenient, accuracy depends on the phone’s calibration and the steadiness of the surface.
For measuring longer distances, such as the grade of a hiking trail or road, GPS-enabled mapping applications provide an alternative method. These apps use stored digital elevation model data or GPS readings to determine the elevation difference between two distant points. The application calculates the slope by dividing the change in elevation (rise) by the horizontal distance (run) between the measured coordinates. This digital approach is limited by the resolution and accuracy of the underlying elevation data.