Authoritative Data Source & Methodology

Primary reference: BIPM — The International System of Units (SI), 9th edition (2019, updates 2022). See the SI definition of the second. All conversions here use 1 minute = 60 seconds, 1 hour = 3,600 seconds, 1 day = 86,400 seconds (no leap seconds). BIPM SI Brochure.

“Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.”

The Formula Explained

Given days \(d\), hours \(h\), minutes \(m\), seconds \(s\):
\[ S = s + 60\,m + 3600\,h + 86400\,d \] Conversely, for a total seconds \(S \ge 0\):
\[ d = \left\lfloor \frac{S}{86400} \right\rfloor,\quad h = \left\lfloor \frac{S \bmod 86400}{3600} \right\rfloor,\quad m = \left\lfloor \frac{S \bmod 3600}{60} \right\rfloor,\quad s = S \bmod 60 \]

Glossary of Variables

  • d — days (0, 1, 2, ...)
  • h — hours (0–23 recommended; may exceed after back-conversion)
  • m — minutes (0–59 recommended)
  • s — seconds (fractional allowed, e.g., 0.125 s)
  • S — total seconds (fractional allowed)
  • HH:MM:SS — timecode format; hours may exceed 24

How It Works: A Step-by-Step Example

Scenario: You have 0 d, 1 h, 2 m, 3 s.

  1. Compute total seconds: \(S = 3 + 60 \cdot 2 + 3600 \cdot 1 + 86400 \cdot 0 = 3723\ \mathrm{s}\).
  2. HH:MM:SS becomes 01:02:03.
  3. Total minutes = \(3723 / 60 = 62.05\) minutes.

Frequently Asked Questions

What about leap seconds and civil time?

This calculator assumes 86,400 seconds per day. Leap seconds are not considered; for astronomical or UTC-level work, use specialized time libraries.

Can I enter fractional hours or minutes?

Yes. Fractional values are supported. They’re internally converted to seconds with up to millisecond precision.

Why does breakdown recommend 0–23 for hours and 0–59 for minutes?

It’s easier to read. The tool will still normalize any totals appropriately when reverse-converting.

Does HH:MM:SS allow hours > 24?

Yes, especially useful for long media or workloads spanning multiple days.

Are negative durations supported?

No, to avoid ambiguity. If you need signed deltas, compute each absolute duration then compare.

Tool developed by Ugo Candido. Content verified by CalcDomain Editorial Board.
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