PPM to Seconds per Day Calculator: Quartz Clock Accuracy

PPM to seconds calculator

Enter a signed frequency offset and an elapsed duration. Positive values mean the clock runs fast; negative values mean it runs slow. For a ± specification, enter its positive magnitude to calculate one side of the error bound.

The formula and conversion table below also let you calculate the result without interactive controls.

The calculator assumes constant offset, zero initial time error and no resynchronization. It uses 86,400 seconds per day. A 30-day result is a fixed interval, and a 365-day result excludes leap days and leap-second adjustments.

The conversion formula

Parts per million expresses fractional frequency offset. Frequency accuracy describes closeness to the intended frequency; stability describes how frequency changes over time or conditions.^[1]

For one day, 86,400 / 1,000,000 = 0.0864. Multiply the signed ppm value by 0.0864 to obtain seconds gained or lost per day.

Worked examples

• +10 ppm for 30 days: 10 × 0.0864 × 30 = +25.92 seconds.
• −20 ppm for 7 days: −20 × 0.0864 × 7 = −12.096 seconds.
• ±0.05 ppm for one day: the calculated bound is ±0.00432 seconds, or ±4.32 milliseconds.

These are arithmetic examples, not measured FCom product results. A ±10 ppm specification describes a permitted range under stated conditions; it does not mean every unit drifts at exactly 10 ppm.

Convert a measured time error back to ppm

If a clock gains 2 seconds over 86,400 reference seconds, its average rate offset is about +23.148 ppm. Subtract any initial clock offset and exclude intervals containing manual adjustments or synchronization.

Quick conversion table

Apply the sign of the frequency offset to these magnitudes. For example, a constant −5 ppm gives −0.432 seconds per day.

Optional tuning-fork temperature estimator

An uncompensated tuning-fork crystal can be approximated near its turnover temperature by a downward parabolic frequency curve. The coefficient and turnover temperature must come from the selected crystal’s data.^[2]

Here, k is negative and expressed in ppm/°C². This model is not a general model for AT-cut crystals, TCXOs or OCXOs. Use it only within the temperature range where the supplier supports the approximation.

Illustrative example: for 0 to 40°C, T₀ = 25°C and k = −0.034 ppm/°C², the largest temperature-shift magnitude is 0.034 × 25² = 21.25 ppm. Adding an initial ±10 ppm tolerance gives a conservative magnitude bound of 31.25 ppm, equivalent to 2.7 seconds per day.

This symmetric bound is conservative: the modeled thermal shift is negative. It assumes the largest error persists throughout the interval. Actual accumulated error depends on time spent at each temperature. Aging, coefficient uncertainty and turnover-temperature tolerance are not included.

Build a complete timing budget

Check what each datasheet limit includes before adding terms. Initial tolerance, temperature variation, load mismatch, supply effects and aging may be separate specifications or already included in a combined limit.^[3]

• Avoid double-counting: do not add an uncompensated temperature curve to a TCXO specification that already covers temperature.
• Use compatible bounds: summing applicable maximum magnitudes gives a conservative budget. Root-sum-square needs justified statistical assumptions; it is not a guaranteed limit.
• Account for correction: calibration and synchronization can reduce accumulated error, but residual rate error and synchronization uncertainty remain.
• Separate rate from noise: ppm alone does not describe jitter, phase noise, startup delay or timestamp latency.

For changing conditions, calculate and add the error over each interval. A single fixed ppm value represents either a constant offset, a measured time-average, or an explicitly chosen bound.