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Battery Life Calculator

Discharge time equals capacity divided by current raised to the Peukert number

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Peukert's Law

Peukert's Law models how a battery's usable capacity drops as you draw more current. An ideal battery has a Peukert number of 1, but real-world lead-acid batteries typically fall between 1.1 and 1.3.

T = C / Iⁿ

How It Works

Peukert's Law models how a battery's usable capacity drops as you draw more current. The formula T = C / Iⁿ accounts for internal losses that worsen at higher discharge rates. An ideal battery has a Peukert number of 1, but real-world lead-acid batteries typically fall between 1.1 and 1.3.

Example Problem

A 100 Ah lead-acid battery with a Peukert number of 1.2 is discharged at 10 A. How long will it last?

  1. Identify the known values: capacity C = 100 Ah, discharge current I = 10 A, Peukert exponent n = 1.2.
  2. Determine what we are solving for: the discharge time T in hours.
  3. Write the Peukert equation: T = C / I^n.
  4. Calculate I raised to the Peukert exponent: I^n = 10^1.2 ≈ 15.85.
  5. Substitute into the formula: T = 100 / 15.85.
  6. Compute the result: T ≈ 6.31 hours. Without the Peukert correction (n = 1) the answer would be 10 hours, so the real runtime is about 37% shorter at this discharge rate.

The Peukert effect becomes more dramatic at higher currents. At 20 A, the same battery would last only about 2.6 hours instead of the naive 5-hour estimate.

When to Use Each Variable

  • Solve for Discharge Time — when you know the battery capacity, discharge current, and Peukert number and need to estimate runtime, e.g., sizing a battery bank for an off-grid cabin.
  • Solve for Capacity — when you know the required runtime and discharge current and need to find the minimum battery capacity, e.g., specifying a UPS battery.
  • Solve for Current — when you know the battery capacity and desired runtime and need the maximum safe discharge current, e.g., setting load limits for a solar system.
  • Solve for Peukert Number — when you have measured discharge times at different currents and need to characterize a battery, e.g., benchmarking a new lead-acid battery model.

Key Concepts

Peukert's Law accounts for the fact that batteries deliver less usable energy at higher discharge rates due to internal resistance and chemical kinetics. The Peukert exponent n quantifies this effect: n = 1 for an ideal battery, n = 1.1-1.3 for lead-acid, and n near 1.0 for lithium-ion. Higher discharge currents cause disproportionately larger capacity losses, making Peukert's correction essential for accurate runtime predictions.

Applications

  • Off-grid solar systems: calculating how long a battery bank will power a load before recharging is needed
  • Electric vehicles: estimating range under different driving conditions (highway vs. city, which draw different currents)
  • UPS sizing: determining how many minutes of backup power a given battery provides at the expected load
  • Marine electronics: planning battery capacity for trolling motors and onboard electronics during fishing trips

Common Mistakes

  • Ignoring the Peukert effect entirely — dividing capacity by current (T = C/I) overestimates runtime for lead-acid batteries by 20-40% at high discharge rates
  • Using the wrong Peukert exponent — lithium-ion batteries have n near 1.0 while lead-acid is 1.1-1.3; applying the wrong value gives inaccurate predictions
  • Forgetting that rated capacity is measured at a specific discharge rate (usually C/20) — drawing more current than the rated test current reduces effective capacity significantly

Frequently Asked Questions

How long will my battery last at a given current draw?

Use Peukert's Law: T = C / I^n. Divide the battery capacity (in Ah) by the discharge current raised to the Peukert exponent. For example, a 100 Ah lead-acid battery (n = 1.2) at 10 A lasts about 6.3 hours, not the 10 hours you would get from simple division.

Why does a battery's actual life differ from the calculated value?

Real-world battery life varies due to temperature, age, depth of discharge, and internal resistance degradation. Cold temperatures increase resistance and reduce capacity by 20-30%. Older batteries have higher internal resistance, which raises the effective Peukert exponent. The calculator gives a theoretical estimate under ideal conditions.

What is the Peukert number for lithium batteries?

Lithium-ion batteries have a Peukert number very close to 1.0 (typically 1.0-1.05), meaning their capacity stays nearly constant regardless of discharge rate. That is one reason lithium batteries outperform lead-acid in high-drain applications.

How do I find my battery Peukert number?

Discharge the battery at two different constant currents and record the times. Then use the Peukert number solver above with the known capacity. Most manufacturers publish this value in the battery datasheet, often listed under performance specifications.

Does temperature affect battery discharge time?

Yes. Cold temperatures increase internal resistance and reduce effective capacity. A 100 Ah battery at 0 degrees C may deliver only 70-80 Ah. Always factor in temperature when sizing batteries for outdoor or winter applications.

What is the C-rate and how does it relate to Peukert's Law?

The C-rate describes how fast a battery is charged or discharged relative to its capacity. A 1C rate discharges a 100 Ah battery at 100 A (fully drained in 1 hour). Peukert's Law explains why high C-rates deliver less total energy — at 2C, a lead-acid battery with n = 1.2 delivers only about 75% of its rated capacity.

Can I use this calculator for rechargeable AA batteries?

Yes. A typical NiMH AA battery has about 2.0-2.5 Ah capacity with a Peukert exponent near 1.05-1.10. Enter the capacity from the label, your expected current draw, and 1.07 as a reasonable Peukert estimate to get the runtime in hours.

Battery Life Formula (Peukert's Law)

Peukert's Law models the relationship between discharge rate and battery runtime:

T = C / In

Where:

  • T — discharge time, measured in hours (h)
  • C — battery capacity, measured in ampere-hours (Ah)
  • I — discharge current, measured in amperes (A)
  • n — Peukert exponent (dimensionless), typically 1.0–1.05 for lithium-ion and 1.1–1.3 for lead-acid

When n = 1, the formula simplifies to T = C / I (ideal battery). As n increases, higher currents cause disproportionately larger capacity losses due to internal resistance and electrochemical kinetics.

Worked Examples

IoT Devices

How long will a sensor node run on a coin cell battery?

A wireless temperature sensor draws 0.5 mA average from a 220 mAh CR2032 coin cell (n ≈ 1.05 for lithium). How many hours will it last?

  • C = 220 mAh = 0.22 Ah, I = 0.5 mA = 0.0005 A, n = 1.05
  • In = 0.00051.05 ≈ 0.000427
  • T = 0.22 / 0.000427 ≈ 515 hours (≈ 21 days)
  • T ≈ 515 hours

Real-world lifetime depends on sleep mode duty cycles — most IoT sensors sleep 99% of the time and can last months or years.

Electric Vehicles

How far can an electric scooter travel on a full charge?

An e-scooter has a 10 Ah lithium battery (n ≈ 1.02) and draws 15 A at full throttle. Estimate the runtime.

  • C = 10 Ah, I = 15 A, n = 1.02
  • In = 151.02 ≈ 15.56
  • T = 10 / 15.56 ≈ 0.643 hours (≈ 39 minutes)
  • T ≈ 0.643 hours

At 25 km/h cruise speed, this gives roughly 16 km range. Lighter throttle extends the range significantly because of the cubic-like Peukert relationship.

Emergency Backup

How long will a UPS keep a server running during a power outage?

A server room UPS uses a 100 Ah lead-acid battery (n = 1.2) drawing 20 A under load. Estimate the backup runtime.

  • C = 100 Ah, I = 20 A, n = 1.2
  • In = 201.2 ≈ 38.34
  • T = 100 / 38.34 ≈ 2.61 hours
  • T ≈ 2.61 hours

Without the Peukert correction (n = 1), the naive estimate would be 5 hours — nearly double. Lead-acid batteries lose substantial capacity at higher discharge rates.

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