For a one-ampere discharge rate, Peukert's law is often stated as
C p = I k t , C_{p}=I^{k}t,}
where:
C p { C_{p}}
is the capacity at a one-ampere discharge rate, which must be expressed in
ampere hours,
I { I}
is the actual discharge current (i.e. current drawn from a load) in amperes,
t { t}
is the actual time to discharge the battery, which must be expressed in
hours.
k {k}
is the Peukert constant
The capacity at a one-ampere discharge rate is not usually given for practical cells. As such, it can be useful to reformulate the law to a known capacity and discharge rate:
t = H ( C I H ) k t=H\left({\frac {C}{IH})^{k}}
where:
H {H}
is the rated discharge time (in hours),
C { C}
is the rated capacity at that discharge rate (in ampere hours),
I { I}
is the actual discharge current (in amperes),
k { k}
is the Peukert constant (dimensionless),
t { t}
is the actual time to discharge the battery (in hours).
Using the above example, if the battery has a Peukert constant of 1.2 and is discharged at a rate of 10 amperes, it would be fully discharged in time 20 ( 100 10 ⋅ 20 ) 1.2 {20{({\frac {100}{10\cdot 20}}\)^{1.2}}}
, which is approximately 8.7 hours. It would therefore deliver only 87 ampere-hours rather than 100.
Peukert's law can be written as
I t = C ( C I H ) k − 1 , It=C\({\frac {C}{IH}}t)^{k-1},}
giving I t {\It}
, which is the effective capacity at the discharge rate I I}
.
Peukert's law, taken literally, would imply that the total charge delivered by the battery ( I t
) goes to infinity as the rate of discharge goes to zero. This is of course impossible, since there is a finite amount of the reactants of the electrochemical reaction on which the battery is based.
If the capacity is listed for two discharge rates, the Peukert exponent can be determined algebraically:
Q Q 0 = ( T T 0 ) k − 1 k
Another commonly used form of the Peukert's law is:
Q Q 0 = ( I I 0 ) α
where:
α = k − 1 2 − k