How to calculate the number of ticks? - briefly
Calculate the total time span, then divide it by the duration of a single tick. The result follows the formula «ticks = floor(total_time / interval) + 1», where the floor function discards any fractional remainder.
How to calculate the number of ticks? - in detail
A tick represents the smallest indivisible unit of measurement in a given system, whether it is a financial price increment, a time‑step in a simulation, or a pixel interval on a graphical axis. Determining the total number of ticks requires three basic inputs: the lower bound of the range, the upper bound of the range, and the size of each tick.
The calculation proceeds as follows:
- Verify that the tick size is positive and that the lower bound is less than the upper bound.
- Compute the raw interval: upper − lower.
- Divide the interval by the tick size: raw ÷ size.
- Apply a ceiling function to the quotient to ensure coverage of the entire range.
- Add one to include the initial tick at the lower bound.
Expressed as a formula, the tick count N is
«N = ⌈(upper − lower) / size⌉ + 1».
When the interval is an exact multiple of the tick size, the ceiling operation yields an integer, and the additional unit accounts for the starting point. For example, with a lower bound of 0, an upper bound of 5, and a tick size of 0.5, the calculation yields
«N = ⌈(5 − 0) / 0.5⌉ + 1 = ⌈10⌉ + 1 = 11»,
producing ticks at 0, 0.5, 1.0, … , 5.0.
Special cases:
- If the tick size does not divide the interval evenly, the final tick will exceed the upper bound by less than one tick size, preserving full coverage.
- For non‑numeric ranges (e.g., dates), convert the bounds to a numeric representation (such as Unix timestamps) before applying the same steps.
Implementations in common programming languages follow the same logic: compute the difference, perform integer division with rounding up, and add the initial element. This method guarantees a consistent and reproducible tick count across diverse applications.