Calculating your slant height is straightforward once you know the Cone Slant Height formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Cone Slant Height Calculator.
What is Cone Slant Height?
The Cone Slant Height calculation tells you your slant height from a few simple inputs. The figure you are solving for here is the slant height.
The Cone Slant Height formula
The core formula is:
Slant height = √(Base radius ^ 2 + Height ^ 2)Here is what each input means:
- Base radius — a number. Example: 3.
- Height — a number. Example: 4.
How to calculate it step by step
- Write down the base radius (for example, 3).
- Write down the height (for example, 4).
- Apply the formula above to get your slant height.
- Double-check the result with the Cone Slant Height Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Base radius | 3 |
| Height | 4 |
| Slant height | 5.000000 |
With base radius of 3 and height of 4, the slant height works out to 5.000000.
Example 2
With base radius of 6 and height of 4, the slant height works out to 7.211103.
| Result | Value |
|---|---|
| Slant height | 7.211103 |
Example 3
With base radius of 1.5 and height of 4, the slant height works out to 4.272002.
| Result | Value |
|---|---|
| Slant height | 4.272002 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Cone Slant Height Calculator does it instantly, for free, with the formula and a worked example built in.
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