Slope Percentage Calculator

Percent grade is rise divided by run, times 100

A percent grade answers one question: how much does the ground climb for every 100 units you travel flat? The formula is rise ÷ run × 100. A hill that climbs 6 feet over 100 feet of ground is a 6% grade, because 6 ÷ 100 = 0.06 and 0.06 × 100 = 6. The same hill climbs 6 inches over 100 inches, or 6 meters over 100 meters, because the units cancel.

The run is the part people get wrong. It is the horizontal distance, not the distance along the pavement. On a 6% grade the difference is small, about 9.5 extra feet per mile, but on a 25% hill the road surface is more than 3% longer than the flat run, and the grade you compute from the sloped distance comes out lower than the real one.

Why 100? Because a percentage is a fraction with 100 as the base, and road engineers picked the base that makes mental math possible. Rise ÷ run gives a decimal slope, and moving the decimal two places to the right turns it into a percent. A sign that says 6% is telling you the hill climbs 6 units for every 100 units of flat travel, in any units you like.

The same slope as a ratio, a percent, an angle and feet per mile

Four trades describe one slope four ways, and every row in this table is the same ground. The ratio form shows up in building codes, the percent form on road signs, the angle on a level app, and feet per mile on a map.

The last column comes from one multiplication. There are 5,280 feet in a mile, and 5,280 ÷ 100 = 52.8, so the climb per mile is 52.8 × the grade. A 10% grade climbs 52.8 × 10 = 528 feet in a mile, which is why a two-mile 10% climb leaves you 1,056 feet higher.

Worked example: a 6% grade sign on a hill road

A road sign that says 6% for the next 5 miles is making a promise you can check. The grade means 6 feet of climb per 100 feet of run, so one mile of that road climbs 52.8 × 6 = 316.8 feet, and five miles climb 5 × 316.8 = 1,584 feet.

The angle behind the sign is smaller than the number suggests. atan(0.06) in degrees is 3.43, so a 6% grade is a 3.43 degree hill. That is the number a phone level or a clinometer shows when you point it up the road.

The road surface is a little longer than the flat run, because it runs along the hypotenuse. Over one mile of flat travel the pavement measures sqrt(5280² + 316.8²) = 5,289.5 feet, so you drive 9.5 feet more than the mile. Your odometer, which counts tire revolutions along the surface, records the longer number. Trip planners that use flat map distance are the ones that are off, and the gap grows on steeper roads.

Fuel and brakes feel grades that eyes barely notice. A 6% climb for five miles is 1,584 feet of lift, and every 100 pounds of trailer on that climb takes measurable extra fuel. Coming down the other side, the same 1,584 feet of drop is what makes engine braking worth using instead of riding the service brakes for five miles.

Why a 10% grade is not 10 degrees

Percent and degrees are two different rulers on the same hill. Percent grade is the tangent of the angle written as a percent, and the tangent curve bends away from a straight line as the angle grows. The two scales agree only at small angles, where the tangent of an angle is close to the angle itself.

The anchor point is 45 degrees, where rise equals run exactly and the grade is 100 percent. Below that, percent runs hotter than degrees: an 8.33% grade is 4.76 degrees, and a 15% grade is 8.53 degrees. Above it, percent leaves degrees behind fast, and a 50% grade is still only 26.57 degrees.

Reading one ruler as the other is the most expensive mistake on this page. A builder who hears "15 percent" and pictures 15 degrees is planning a slope more than 1.7 times steeper than the one described, and a ramp at 15 degrees fails inspection in every jurisdiction in the country.

Where percent grades show up

Most percent grades you meet are set by a code or a standard, and the numbers are worth knowing on sight because they come up in arguments with contractors and in permit drawings.

Notice the gap between 2% and 8.33%. Drainage wants slope, accessibility caps it, and everything between those two numbers is a design negotiation. A patio at 1% holds puddles, and a walkway at 10% fails as an accessible route.

How to measure the grade where you stand

The cheapest accurate method needs a 4-foot level and a tape measure. Set one end of the level on the high ground and lift the low end until the bubble centers. Measure the gap under the lifted end in inches. The rise is that gap, the run is 48 inches, and the grade is the rise ÷ 48 × 100.

A gap of 2 inches under the level gives 2 ÷ 48 = 0.0417, or about 4.2%. A gap of 5 inches gives 5 ÷ 48 = 0.104, or 10.4%. If you want the grade over a longer run for a smoother answer on bumpy ground, use a straight 8-foot board and divide by 96 instead.

Phone apps work well enough for planning. A clinometer app measures the angle directly, and the grade is the tangent × 100: 4 degrees is a 7% grade, 6 degrees is 10.5%. Lay the phone flat against a straight board resting on the ground rather than trusting the case edges.

Two habits keep field measurements honest. First, keep the run horizontal, which is automatic with a level but not with a tape stretched along the ground. Second, measure the run and the rise in the same units, because a rise in inches over a run in feet comes out twelve times too steep.

Six mistakes that skew the number

The averaging error is the one that surprises people with real money. A road that drops 6% for a mile and 2% for the next three miles climbs 316.8 + 3 × 105.6 = 633.6 feet over 4 miles, which is a 3% grade for the whole run, not the 4% that averaging the two numbers suggests. The gentle miles carry more distance, so they weigh more.

The run over rise mistake is the mirror image. It gives the ratio, which is the form building codes use, so a 6% grade and a 1:16.67 ramp are the same hill written two ways. Saying "a grade of 16.67" is wrong by a factor of 2.78, and on a ramp that is the difference between pass and fail.

Grade from elevation gain on a map or a trail app

Maps and trail apps hand you two numbers: elevation gain and distance. The grade is gain ÷ distance × 100, with one care: the distance is measured along the path, which is the sloped length, not the flat run.

A trail that gains 1,000 feet over 2 miles has a run of 10,560 feet along the surface, so 1,000 ÷ 10,560 = 0.0947, or about 9.5%. The true horizontal run is slightly shorter, sqrt(10560² − 1000²) = 10,512.6 feet, which would give 9.51%. The two answers differ by four hundredths of a point, so for hiking the distinction is not worth a second calculation.

Grade is why two trails with the same summit can feel like different mountains. A 3,000-foot climb spread over 6 miles is a 9.5% average grade, while the same 3,000 feet over 12 miles is 4.7%. Average grade also hides the steep stretches, which is why a trail rated moderate can still hold a half-mile section at 20%.

Watch the distance source. GPS tracks on a phone wander on switchbacks and under tree cover, and a track that shortcuts the switchbacks reports less distance and a steeper grade than you climbed. Map-measured trail distance is the steadier input.