Practice · Grade 7 Percentages
Slope Percentage — Practice
Practice problems on percent grade in rising difficulty plus one boss question. Use rise ÷ run · 100, with a hint and worked solution for each. Free.
Q1 of 6
0 correct
Find the slope in percent.
5 m rise / 100 m run
Quick answer
What is the best way to practise slope in percent?
Work through at least five problems in rising difficulty. Always use the same formula: rise ÷ run · 100. Start with round runs such as 100 m or 50 m, then move to problems where you first reduce the ratio (e.g. 9 ÷ 12 = 0.75), and finish with a case where the rise is greater than the run — there the grade is above 100%. Write down every step and check your answer with the calculator.
HowTo
A 4-step solving strategy
This order works for any problem made of a rise and a horizontal run.
- 1Step 1 of 4
Write down rise and run
Note the rise (height difference) and the horizontal run in the same unit. Make sure the run is the horizontal distance, not the sloped path length.
- 2Step 2 of 4
Divide rise by run
Form the ratio rise ÷ run. For 3 m over 4 m: 3 ÷ 4 = 0.75. Reducing helps: 9 ÷ 12 is the same as 3 ÷ 4.
- 3Step 3 of 4
Multiply by 100
The ratio times 100 gives the percent grade. 0.75 · 100 = 75%. If the rise exceeds the run, you go above 100%.
- 4Step 4 of 4
Sanity-check the result
If the rise is half the run, you should get about 50%. When rise and run are equal it is exactly 100% (which is 45°).
Examples
Worked practice examples
Four typical problems. Try each yourself first, then compare with the solution.
Easy
Slope in percent: 5 m over 100 m
5 ÷ 100 = 0.05
0.05 · 100 = 5%
Angle: arctan(0.05) ≈ 2.86°
With a 100 m run, the percentage is just the rise in metres.
Medium
Slope in percent: 3 m over 4 m
3 ÷ 4 = 0.75
0.75 · 100 = 75%
Angle: arctan(0.75) ≈ 36.87°
The rise is smaller than the run, so the grade stays below 100%.
Hard
Slope in percent: 10 m over 8 m
10 ÷ 8 = 1.25
1.25 · 100 = 125%
Angle: arctan(1.25) ≈ 51.34° (more than 45°)
Rise greater than run → grade above 100% and angle above 45°.
Hard
Slope in percent: 9 m over 12 m
9 ÷ 12 = 0.75
0.75 · 100 = 75%
Angle: arctan(0.75) ≈ 36.87°
9 ÷ 12 reduces to 3 ÷ 4 — same result as above.
Pitfalls
Common mistakes — and how to avoid them
These five traps show up again and again with percent grade.
Percent confused with degrees
A 15% grade is not 15° but ≈ 8.53°. Percent and angle measure the same ratio differently — convert via arctan.
Using the sloped path instead of the run
The grade uses the horizontal run, not the sloped path length (hypotenuse). Otherwise you get too small a value.
Forgetting to multiply by 100
3 ÷ 20 = 0.15 is not yet the answer. Only 0.15 · 100 = 15% is the percent grade.
Reading 100% as vertical
100% means rise equals run, i.e. 45° — not a vertical wall. Above 100% is perfectly normal when the rise is larger.
Mixing different units
Rise in centimetres and run in metres gives nonsense. Convert both distances to the same unit first.
Study
Practise with a plan — three short tips
Start with round runs
Problems with a 100 m or 50 m run make mental maths easy and cement the formula. Then progress to values you have to reduce first.
Solve first, then check the solution
Write down your working before revealing the hint. Active recall is far more effective for learning than passive reading.
Check the result with the calculator
Enter rise and run into the slope calculator and compare the percentage and angle with your answer — that pinpoints mistakes instantly.
FAQ
Practice FAQ
Glossary
Terms in one sentence
- Slope in percent
- The ratio rise ÷ run expressed per 100 (i.e. times 100).
- Rise
- The vertical height difference between the start and end of the path.
- Run
- The horizontal distance — not the sloped length.
- Slope angle
- The angle to the horizontal: α = arctan(rise ÷ run).
- Downgrade
- A negative slope — downhill instead of uphill, same formula.
- Arctangent
- The inverse of the tangent; turns a ratio into an angle.
- Boss question
- The last and hardest problem in a practice set.