Minutes to Decimal Chart
By Time Calculator · · Data version 1.0.0
Divide minutes by 60 to get decimal hours. The chart below gives every whole minute from 0 to 60 as an exact fraction and at three display precisions. For example, 45 minutes is exactly 0.75 hours; 20 minutes is exactly ⅓ hour, displayed as 0.33 at two decimal places.
For a mixed duration or a conversion in the other direction, use the hours to decimal calculator.
0–60 minutes to decimal hours
Use the fraction column when you need the exact value. All decimal columns round to the nearest value at the stated number of places; exact halfway cases round upward. An equals sign means that the displayed decimal is exact; ≈ means it is rounded.
| Minutes | Exact hours | 2 places | 3 places | 4 places |
|---|---|---|---|---|
| 0 | 0 | = 0.00 | = 0.000 | = 0.0000 |
| 1 | 1/60 | ≈ 0.02 | ≈ 0.017 | ≈ 0.0167 |
| 2 | 1/30 | ≈ 0.03 | ≈ 0.033 | ≈ 0.0333 |
| 3 | 1/20 | = 0.05 | = 0.050 | = 0.0500 |
| 4 | 1/15 | ≈ 0.07 | ≈ 0.067 | ≈ 0.0667 |
| 5 | 1/12 | ≈ 0.08 | ≈ 0.083 | ≈ 0.0833 |
| 6 | 1/10 | = 0.10 | = 0.100 | = 0.1000 |
| 7 | 7/60 | ≈ 0.12 | ≈ 0.117 | ≈ 0.1167 |
| 8 | 2/15 | ≈ 0.13 | ≈ 0.133 | ≈ 0.1333 |
| 9 | 3/20 | = 0.15 | = 0.150 | = 0.1500 |
| 10 | 1/6 | ≈ 0.17 | ≈ 0.167 | ≈ 0.1667 |
| 11 | 11/60 | ≈ 0.18 | ≈ 0.183 | ≈ 0.1833 |
| 12 | 1/5 | = 0.20 | = 0.200 | = 0.2000 |
| 13 | 13/60 | ≈ 0.22 | ≈ 0.217 | ≈ 0.2167 |
| 14 | 7/30 | ≈ 0.23 | ≈ 0.233 | ≈ 0.2333 |
| 15 | 1/4 | = 0.25 | = 0.250 | = 0.2500 |
| 16 | 4/15 | ≈ 0.27 | ≈ 0.267 | ≈ 0.2667 |
| 17 | 17/60 | ≈ 0.28 | ≈ 0.283 | ≈ 0.2833 |
| 18 | 3/10 | = 0.30 | = 0.300 | = 0.3000 |
| 19 | 19/60 | ≈ 0.32 | ≈ 0.317 | ≈ 0.3167 |
| 20 | 1/3 | ≈ 0.33 | ≈ 0.333 | ≈ 0.3333 |
| 21 | 7/20 | = 0.35 | = 0.350 | = 0.3500 |
| 22 | 11/30 | ≈ 0.37 | ≈ 0.367 | ≈ 0.3667 |
| 23 | 23/60 | ≈ 0.38 | ≈ 0.383 | ≈ 0.3833 |
| 24 | 2/5 | = 0.40 | = 0.400 | = 0.4000 |
| 25 | 5/12 | ≈ 0.42 | ≈ 0.417 | ≈ 0.4167 |
| 26 | 13/30 | ≈ 0.43 | ≈ 0.433 | ≈ 0.4333 |
| 27 | 9/20 | = 0.45 | = 0.450 | = 0.4500 |
| 28 | 7/15 | ≈ 0.47 | ≈ 0.467 | ≈ 0.4667 |
| 29 | 29/60 | ≈ 0.48 | ≈ 0.483 | ≈ 0.4833 |
| 30 | 1/2 | = 0.50 | = 0.500 | = 0.5000 |
| 31 | 31/60 | ≈ 0.52 | ≈ 0.517 | ≈ 0.5167 |
| 32 | 8/15 | ≈ 0.53 | ≈ 0.533 | ≈ 0.5333 |
| 33 | 11/20 | = 0.55 | = 0.550 | = 0.5500 |
| 34 | 17/30 | ≈ 0.57 | ≈ 0.567 | ≈ 0.5667 |
| 35 | 7/12 | ≈ 0.58 | ≈ 0.583 | ≈ 0.5833 |
| 36 | 3/5 | = 0.60 | = 0.600 | = 0.6000 |
| 37 | 37/60 | ≈ 0.62 | ≈ 0.617 | ≈ 0.6167 |
| 38 | 19/30 | ≈ 0.63 | ≈ 0.633 | ≈ 0.6333 |
| 39 | 13/20 | = 0.65 | = 0.650 | = 0.6500 |
| 40 | 2/3 | ≈ 0.67 | ≈ 0.667 | ≈ 0.6667 |
| 41 | 41/60 | ≈ 0.68 | ≈ 0.683 | ≈ 0.6833 |
| 42 | 7/10 | = 0.70 | = 0.700 | = 0.7000 |
| 43 | 43/60 | ≈ 0.72 | ≈ 0.717 | ≈ 0.7167 |
| 44 | 11/15 | ≈ 0.73 | ≈ 0.733 | ≈ 0.7333 |
| 45 | 3/4 | = 0.75 | = 0.750 | = 0.7500 |
| 46 | 23/30 | ≈ 0.77 | ≈ 0.767 | ≈ 0.7667 |
| 47 | 47/60 | ≈ 0.78 | ≈ 0.783 | ≈ 0.7833 |
| 48 | 4/5 | = 0.80 | = 0.800 | = 0.8000 |
| 49 | 49/60 | ≈ 0.82 | ≈ 0.817 | ≈ 0.8167 |
| 50 | 5/6 | ≈ 0.83 | ≈ 0.833 | ≈ 0.8333 |
| 51 | 17/20 | = 0.85 | = 0.850 | = 0.8500 |
| 52 | 13/15 | ≈ 0.87 | ≈ 0.867 | ≈ 0.8667 |
| 53 | 53/60 | ≈ 0.88 | ≈ 0.883 | ≈ 0.8833 |
| 54 | 9/10 | = 0.90 | = 0.900 | = 0.9000 |
| 55 | 11/12 | ≈ 0.92 | ≈ 0.917 | ≈ 0.9167 |
| 56 | 14/15 | ≈ 0.93 | ≈ 0.933 | ≈ 0.9333 |
| 57 | 19/20 | = 0.95 | = 0.950 | = 0.9500 |
| 58 | 29/30 | ≈ 0.97 | ≈ 0.967 | ≈ 0.9667 |
| 59 | 59/60 | ≈ 0.98 | ≈ 0.983 | ≈ 0.9833 |
| 60 | 1 | = 1.00 | = 1.000 | = 1.0000 |
Download this 61-row chart as CSV. To convert 90 minutes, keep the full duration: 90 ÷ 60 = 1.5 hours.
How to convert hours, minutes and seconds
One minute is 60 seconds and one hour is 3,600 seconds. These unit ratios appear in NIST Table 6 and the BIPM SI Brochure. Expressing the duration in hours gives:
Decimal hours = H + M ÷ 60 + S ÷ 3600
Here H, M and S are the hour, minute and second parts of a duration. For 2 hours 45 minutes 30 seconds: 2 + 45/60 + 30/3600 = 331/120 hours ≈ 2.7583 hours. Add the fractional parts before rounding.
1:30 is different from 1.30 hours
When the colon separates hours and minutes, 1:30 means 1 hour 30 minutes, or 1.5 hours. The decimal 1.30 hours means 1 hour plus 0.30 × 60 minutes: 1 hour 18 minutes. Write the unit and format with the number.
Convert decimal hours back to time
Multiply by 3,600 to get seconds, then split into hours, minutes and seconds. For 1.25 hours, 1.25 × 3600 = 4500 seconds = 1 hour 15 minutes. If you need whole seconds, round once before splitting. The precision comparison below uses nearest-second rounding, with exact halves upward.
What precision do decimal hours preserve?
We enumerated all 86,401 whole-second durations from 0 through 86,400 seconds inclusive, at each of 2, 3 and 4 decimal places. For each duration, we compared the exact seconds with the seconds represented by its rounded decimal, then rounded that represented value back to the nearest whole second.
| Decimal places | Display step | Largest display error | Changed round trips | Largest round-trip error |
|---|---|---|---|---|
| 2 | 36 s | 18 s | 84,000 / 86,401 | 18 s |
| 3 | 3.6 s | 1.8 s | 62,400 / 86,401 | 2 s |
| 4 | 0.36 s | 0.16 s | 0 / 86,401 | 0 s |
On a small screen, scroll the results table sideways to see all five columns.
Four decimal places recovered every original whole second in this corpus. This does not make the decimal display exact: only 9,601 of the 86,401 four-place displays represent the original seconds exactly. It also does not make sums of those displays exact.
Why is the four-place maximum 0.16 seconds?
A four-place step is 0.0001 hour, or 0.36 second. Half a step is 0.18 second, an upper bound for arbitrary inputs. Our inputs are restricted to whole seconds. On that grid, errors occur in multiples of 0.04 second; the largest observed magnitude is 0.16 second. For example, 2 seconds becomes 0.0006 hours = 2.16 seconds, which rounds back to 2 seconds.
At two places, 18 seconds becomes 0.01 hours = 36 seconds, a display and round-trip error of +18 seconds. At three places, 9 seconds becomes 0.003 hours = 10.8 seconds, then 11 seconds on the return trip: +1.8 seconds in the display and +2 whole seconds after recovery.
Add original durations before rounding
Three 20-minute entries total exactly 60 minutes. Rounding each entry to 0.33 hours first gives 0.99 hours, or 59 minutes 24 seconds: 36 seconds less than the exact total.
Even four places can accumulate error: thirty one-minute entries, each displayed as 0.0167 hours, sum to 0.5010 hours. The exact total is 0.5000 hours, a difference of 3.6 seconds. A single-value round trip and a sum of rounded values are different tests.
Keep whole seconds or exact fractions while adding, then round the final result to the precision you need. The seven-day time card calculator totals original seconds before formatting the weekly decimal.
Method, data and reproducibility
This is a deterministic arithmetic comparison, not a survey of users or a test of other calculators. The original contribution is the versioned comparison matrix, complete row results and reproducible code. The unit ratios are established facts.
- For each integer n from 0 through 86,400, form the exact ratio n/3600 hours.
- At precision p, scale by 10p, round to the nearest integer (exact halves upward), then divide by 10p.
- Multiply the rounded ratio by 3,600. Record its signed difference from n as the display error.
- Round the represented seconds to a whole second with the same rule. Record the difference from n as the round-trip error.
- Report each maximum absolute error and count every changed round trip. Include both endpoints.
The downloadable Python program uses integers and fractions.Fraction. An independent BigInt implementation checks every exported row in the website tests. Neither reference calculation relies on binary floating-point rounding.
- Minute chart · CSV — 61 rows, exact fractions and 2/3/4-place displays.
- Complete comparison · compressed CSV — 259,203 rows; exact signed errors and recovered seconds.
- Results · JSON — maxima, counts, scope and worked aggregation examples.
- Recomputation program · Python — Python 3.9 or later; standard library only.
- Generated file checksums · SHA-256 — verify the chart, corpus and results.
- Method and column definitions · JSON, source map · JSON, limitations · JSON.
Save the program, then run python3 recompute.py --output ./recomputed. The chart CSV and results JSON should match this version byte for byte. Compare the complete corpus after decompression: Python and zlib versions can change gzip container bytes. The published checksums verify the downloaded files. Errors in the corpus use reduced fractions of a second, such as 4/25 for 0.16 second.
What the results cover
The enumeration covers nonnegative whole seconds up to 24 hours and the stated rounding rule. It does not evaluate negative or subsecond inputs, longer durations, parsers or the floating-point behavior of a particular programming language. It describes elapsed durations, not time zones, daylight-saving changes or clock readings.
Decimal display precision is separate from rounding a recorded interval to a 5-, 6- or 15-minute increment. This page does not specify payroll or billing rules. Decimal hours here retain the ordinary 3,600-second hour; they are not the ten-hour day of French Revolutionary decimal time.
Sources, citation and reuse
- NIST, Guide to the SI, Chapter 5, Table 6. Source for 1 min = 60 s and 1 h = 3,600 s.
- BIPM, The International System of Units, 9th edition, updated 2026, Table 8. Primary source for unit conversion coefficients. See also the June 2026 clarification of non-SI unit status. Minute and hour are non-SI units; this page uses their numerical ratios without adopting older status labels.
The precision findings are our calculations, not findings or endorsements attributed to NIST or BIPM. For unit definitions, cite those original publications. For this comparison, cite the precision results, version and method together.
Time Calculator. “Minutes to Decimal Chart: Exact Hours and Rounding.” Version 1.0.0, October 29, 2026. https://time-calculator.dev/minutes-to-decimal-chart#precision-results
Original generated data and the recomputation program are released under CC0 1.0. External source publications retain their own rights. Attribution to the version is welcome and helps others reproduce a result.
Corrections and version history
Version 1.0.0 · October 29, 2026: first chart and full precision comparison. Report an issue through Contact Time Calculator, including the version, input and expected result. Method or corpus changes will receive a new data version; corrections will be described here.