Systems Engineering Calculators
Reliability math, Amdahl, Little's law, and the arithmetic of large systems.
- CIDR Subnet CalculatorTurn an IPv4 address and prefix length into network, broadcast, host range, and usable host count.network = IP AND mask , mask = 0xFFFFFFFF << (32 − prefix) , broadcast = network OR ~mask , hosts = 2^(32−prefix) − 2
- TCP Bandwidth-Delay Product & WindowSize the TCP receive window for a fat pipe — get the bandwidth-delay product and whether window scaling is required.BDP = bandwidth × RTT , max throughput = window / RTT , scaling required when BDP > 65 535 bytes
- Amdahl's Law SpeedupPredict the ceiling on speedup when you only parallelize (or accelerate) part of a workload.S(N) = 1 / [ (1 − p) + p/N ] , S_max = 1 / (1 − p)
- Gustafson-Barsis Scaled SpeedupEstimate parallel speedup when the problem grows with the processor count — the optimistic counterpoint to Amdahl.S(N) = s + (1 − s)·N = N − s·(N − 1)
- M/M/1 QueueAverage wait, queue length, and utilization for a single-server queue with Poisson arrivals and exponential service.ρ = λ/μ, W = 1/(μ−λ), Wq = ρ/(μ−λ), L = ρ/(1−ρ), Lq = ρ²/(1−ρ)
- Little's Law (L = λW)Relate items in a system, arrival rate, and time-in-system — solve for whichever one you don't have.L = λ · W
- RAID Usable CapacityUsable storage, efficiency, and fault tolerance for RAID 0/1/5/6/10 given drive count and size.RAID0: N·S , RAID1: 1·S , RAID5: (N−1)·S , RAID6: (N−2)·S , RAID10: (N/2)·S
- Serial/Parallel System MTBFRoll up component failure rates into a system MTBF for series or active-parallel redundancy.Series: λ_sys = Σλᵢ, MTBF = 1/λ_sys , Parallel(n identical): MTBF = (1/λ)·Σ_{k=1}^{n} 1/k , R_series = ∏Rᵢ, R_parallel = 1 − ∏(1−Rᵢ)
- Utilization Law (ρ = λS)Find how busy a server or resource is from its arrival rate and mean service time.ρ = λ · S / c (single server: ρ = X · S = λ · S)
- Availability (MTBF / MTTR)Steady-state availability of a repairable system from its mean time between failures and mean time to repair.A = MTBF / (MTBF + MTTR)
- Series/Parallel System ReliabilityCombine identical block reliabilities into a series chain, a parallel (redundant) bank, or a k-out-of-n voting group.Series: R = Rⁿ , Parallel: R = 1 − (1−R)ⁿ , k-of-n: R = Σ_{i=k}^{n} C(n,i)·Rⁱ·(1−R)^{n−i}