Introduction
Cosmic rays are high-energy particles from space that interact with Earth’s atmosphere and generate secondary particles (notably neutrons). When these particles pass through semiconductor devices, they can deposit charge in a memory cell and change a stored 0 to a 1 (or vice versa). This event is commonly called a single event upset (SEU) and is a type of soft error: the hardware is not permanently damaged, but the stored data may be corrupted.
This calculator estimates the probability that at least one bit flip occurs in a memory array over a chosen operating time. It is intended for scenario comparison (for example, sea level vs. high altitude, or small memory vs. large memory) rather than for certification-grade reliability analysis.
How to use the calculator
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Enter Memory Size (MB) for the memory region you care about. This tool treats “MB” as mebibytes (MiB) in the computation (1 MB = 1,048,576 bytes), matching the common binary sizing used in computing.
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Enter Operation Time (hours) for how long the memory is exposed (continuous runtime).
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Enter Altitude Above Sea Level (meters). Higher altitude generally means less atmospheric shielding and a higher particle flux.
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Enter the Soft Error Rate per bit per hour at sea level. If you have a vendor SER/FIT figure, convert it to a per-bit-hour rate before using it.
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Select Compute Probability to see the probability of at least one bit flip during the interval.
Tip: Use the calculator to compare two scenarios by changing one input at a time (for example, keep memory size and SER fixed and vary altitude). The output is a probability for the whole memory region, not for a single bit.
Formula and assumptions
The calculation assumes bit flips occur independently with a constant average rate, so the number of flips in a time window follows a Poisson distribution. The steps are:
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Convert memory size to number of bits:
N = memoryMB × 8 × 1024 × 1024
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Apply an altitude multiplier using an exponential approximation:
altitudeFactor = e^(h / 6000)
where h is altitude in meters. This roughly corresponds to a strong increase with altitude (often described as “doubling every ~6 km” in simplified discussions).
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Compute the expected number of flips (Poisson mean):
λ = SER × N × t × altitudeFactor
where SER is the sea-level soft error rate per bit-hour and t is time in hours.
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Convert λ to the probability of at least one flip:
P(at least one) = 1 − e^(−λ)
What this means in practice: if λ is small (much less than 1), the probability is approximately λ. If λ is large, the probability approaches 100%.
Worked example
Suppose you have 512 MB of memory operating for 24 hours at 0 m altitude, and you assume a sea-level soft error rate of 1e-12 per bit-hour.
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Bits: N = 512 × 8 × 1024 × 1024 = 4,294,967,296 bits
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Altitude factor at 0 m: e^(0/6000) = 1
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Expected flips: λ = 1e-12 × 4.294967296e9 × 24 ≈ 0.103
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Probability: P = 1 − e^(−0.103) ≈ 0.098 → about 9.8%
Interpretation: a ~9.8% chance of at least one raw bit flip in that memory region over one day does not automatically mean a user-visible failure. Systems with error detection/correction (ECC), redundancy, memory scrubbing, or application-level checksums can reduce the chance that a flip becomes an incorrect result.
Limitations and practical notes
This calculator is intentionally simple. It is useful for intuition and rough comparisons, but it does not capture all real-world effects. Key limitations include:
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Altitude model is approximate. Real particle flux depends on geomagnetic latitude, shielding, building materials, aircraft routing, and solar conditions. The exponential factor is a convenient approximation, not a calibrated radiation transport model.
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SER is highly device- and workload-dependent. Different memory technologies (SRAM, DRAM, NAND flash), process nodes, voltages, temperatures, and packaging can change susceptibility.
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Independence and constant-rate assumptions. The Poisson model assumes independent events and a constant average rate. Bursts during solar events or correlated multi-bit upsets are not represented.
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“At least one flip” is not the same as “system failure.” ECC, parity, RAID, checksums, retries, and scrubbing can prevent a flip from causing incorrect output.
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Memory size interpretation. The calculator treats the input as the number of bytes actively at risk. If only a portion of memory is used or powered, adjust the MB accordingly.
If you need engineering-grade predictions (for avionics, medical devices, or space systems), use component-specific SER data and an environment model appropriate to your location and shielding, and consider multi-bit upset rates and mitigation coverage.
Understanding the calculation
Cosmic rays constantly bombard Earth. Most are deflected by the magnetic field or absorbed by the atmosphere, yet a fraction of secondary particles reach the surface. When one of these particles interacts with a semiconductor memory cell, it can deposit enough charge to change the stored state. These events are rare for any single bit, but modern devices contain billions of bits and run for long periods, so the chance of observing at least one upset becomes meaningful.
The calculator focuses on the probability of at least one flip because that is often the first question asked in reliability planning: “What is the chance something happens at all during this mission time?” Under the Poisson model, the probability of zero flips is e^(−λ), so the probability of one or more flips is 1 − e^(−λ). This is a standard approach for independent rare events.
The soft error rate (SER) input is the most important and also the most uncertain parameter. Vendors may publish SER in FIT (failures in time), where 1 FIT = 1 failure per 109 device-hours. Converting FIT to a per-bit-hour rate requires knowing what the FIT figure refers to (per device, per megabit, etc.). If you do not have a measured SER for your exact component and environment, treat the output as a sensitivity study rather than a prediction.
Altitude matters because the atmosphere provides shielding. At higher elevations, there is less air mass above you, so more energetic secondaries reach the device. Aircraft cruising altitudes can experience much higher neutron flux than sea level, and high mountain observatories can also see elevated rates. Conversely, underground facilities can have significantly reduced rates. The exponential altitude factor used here is a simplified curve that helps illustrate the trend.
Approximate altitude multipliers (exponential model)
The following table shows the multiplier applied to the sea-level SER using the model altitudeFactor = e^(h/6000). These are illustrative values to help you sanity-check inputs.
| Altitude (m) |
Rate Multiplier |
| 0 |
1.00 |
| 1500 |
1.28 |
| 3000 |
1.65 |
| 6000 |
2.72 |
| 12000 |
7.39 |
Mitigation context (why the raw probability is not the whole story)
Many systems reduce the impact of soft errors with error-correcting codes (ECC). ECC adds redundancy so that a single-bit error can be corrected (and often multi-bit errors can be detected). In addition, memory scrubbing periodically reads and corrects memory to prevent errors from accumulating. At the application level, checksums, retries, and redundant computation can further reduce the chance that a raw bit flip becomes an incorrect output.
In high-altitude and aerospace contexts, designers may use radiation-hardened components, shielding, or redundancy techniques such as triple modular redundancy (TMR), where computations are performed three times and a majority vote determines the result. Space environments can be far more complex than the simplified altitude model used here; this page is best viewed as an educational estimator for terrestrial and near-terrestrial comparisons.
From a statistical perspective, if you want more detail than “at least one,” the Poisson distribution also provides the probability of exactly k flips: (λk/k!)·e^(−λ). When λ exceeds 1, multiple flips become likely, and mitigation strategies must consider multi-bit upsets and the time between scrubbing cycles.
The practical takeaway is that reliability is probabilistic. Even when individual events are rare, scale (lots of bits) and time (long runtimes) can make them relevant. Use this calculator to build intuition, compare environments, and motivate appropriate mitigation (ECC, scrubbing, redundancy, and validation) for the consequences of an error in your system.
