Calculator Inputs
Use measured times, Amdahl estimation, Gustafson scaling, or an overhead-aware model.
Example Data Table
Sample scenario: serial fraction = 10% and serial runtime = 120 seconds.
| Processors | Amdahl Speedup | Gustafson Speedup | Efficiency (%) | Predicted Time (s) |
|---|---|---|---|---|
| 1 | 1.0000 | 1.0000 | 100.00 | 120.0000 |
| 2 | 1.8182 | 1.9000 | 90.91 | 66.0000 |
| 4 | 3.0769 | 3.7000 | 76.92 | 39.0000 |
| 8 | 4.7059 | 7.3000 | 58.82 | 25.5000 |
| 16 | 6.4000 | 14.5000 | 40.00 | 18.7500 |
| 32 | 7.8049 | 28.9000 | 24.39 | 15.3750 |
Formula Used
Basic Speedup
Speedup = T1 / Tp
T1 is serial runtime. Tp is parallel runtime on p processors.
Efficiency
Efficiency = Speedup / p
Efficiency shows how well the processor pool is used.
Amdahl’s Law
Speedup = 1 / (s + (1 - s) / p)
s is the serial fraction. This model assumes fixed problem size.
Gustafson’s Law
Speedup = p - s × (p - 1)
This model is useful when workload size scales with processor count.
Karp–Flatt Metric
e = ((p / Speedup) - 1) / (p - 1)
This estimates the effective serial part from measured performance.
Overhead Model
Tp = T1 × s + T1 × (1 - s) / p + To
To represents startup, communication, or synchronization overhead.
How to Use This Calculator
- Choose a calculation mode that matches your data or assumption.
- Enter processor count and any required runtime values.
- Provide serial fraction when using theoretical or overhead-based models.
- Set graph range and decimal precision for cleaner reporting.
- Press Calculate to show the result summary above the form.
- Use CSV or PDF export when you need a shareable report.
FAQs
1) What does speedup mean here?
Speedup compares one-processor runtime with parallel runtime. A value of 4 means the parallel version completes the same work four times faster than the serial version.
2) Why is efficiency important?
Efficiency shows how much of each processor is doing useful work. Low efficiency often signals communication overhead, imbalance, memory contention, or too much serial work.
3) When should I use measured mode?
Use measured mode when you already know serial and parallel runtimes. It gives direct speedup, utilization, runtime savings, and an estimated serial fraction from real performance.
4) When is Amdahl’s law better?
Amdahl’s law is better for fixed-size workloads. It highlights the upper speedup limit caused by the serial portion, even when processor count keeps increasing.
5) When is Gustafson’s law better?
Use Gustafson’s law when problem size grows with available processors. It often gives a more optimistic view for large simulations, analytics, and scalable batch jobs.
6) What is the Karp–Flatt metric?
It estimates the effective serial fraction from observed speedup. This helps you see whether limited scaling comes from unavoidable serial code or growing parallel overhead.
7) Why can speedup be less than processor count?
Perfect linear scaling is rare. Serialization, synchronization, memory limits, I/O waits, load imbalance, and communication costs all reduce practical speedup below the ideal line.
8) What does the overhead model add?
It adds explicit parallel overhead time to the runtime formula. That makes estimates more realistic for workloads with setup cost, data transfers, barriers, or message passing.