LibraryReferenceEarthing

Tolerable body current

The tolerable body current is the largest current a person of a given weight tolerates for the duration of a shock (IEEE Std 80-2013 §5.3). It is the starting point of the tolerable touch and step voltages, the limits an earth mat is designed to.

1The current a body tolerates

IEEE Std 80-2013 sets the tolerable current from the fibrillation threshold of the body. The current is inversely proportional to the square root of the shock time, with one constant for a person of 50 kg and another for a person of 70 kg.

I_{B, 50} = \frac{0.116}{t _{s}}

(1)

IEEE Std 80-2013 §5.3, Eq. 6

I_{B, 70} = \frac{0.157}{t _{s}}

(2)

IEEE Std 80-2013 §5.3, Eq. 7

where
$I_{B, 50}$ , $I_{B, 70}$	body current a person of 50 kg or 70 kg tolerates	A
$t_{s}$	duration of the shock current	s

A shorter shock is tolerated at a higher current (Figure 1). The shock time is the fault clearing time a person is exposed to. The design takes 0.5 s by default, the backup protection's clearing time, unless a protection study gives less.

Shock time0.75 s · 70 kg: 0.18 A · 50 kg: 0.13 A

Figure 1.The tolerable body current falls as the shock time rises, for persons of 50 kg and 70 kg. The design service calculated the values by Eq. (1) and Eq. (2).

2From current to voltage

The tolerable voltage is the body current times the resistance of its path. IEEE Std 80-2013 takes the body's resistance as 1000 Ω and the contact resistance of one foot on the surface layer as $3 C_{s} ρ_{s}$ (§7). In a touch, the current runs from the hand to both feet, which are in parallel: their resistance is $1.5 C_{s} ρ_{s}$ . In a step, it runs from one foot to the other, through both feet in series: $6 C_{s} ρ_{s}$ (Step voltage).

E_{touch50} = (1000 + 1.5 C_{s} ρ_{s}) \frac{0.116}{t _{s}}

(3)

IEEE Std 80-2013 §8.3, Eq. 32

E_{step50} = (1000 + 6 C_{s} ρ_{s}) \frac{0.116}{t _{s}}

(4)

IEEE Std 80-2013 §8.3, Eq. 29

where
$E_{touch50}$ , $E_{step50}$	tolerable touch and step voltage for a person of 50 kg	V
$C_{s}$	surface layer derating factor (Surface layer and Cs)
$ρ_{s}$	resistivity of the surface layer	Ω·m

The equations for a person of 70 kg take 0.157 in place of 0.116 (Eq. 33 and 30). The design checks the IEC + CEA / CBIP set's mats against the limits for 50 kg and reports those for 70 kg beside them. The ANSI / IEEE set checks against the limits for 70 kg.

Example 1The tolerable voltages of the default 220 kV project

Given a shock time of 0.5 s, a surface layer of 3000 Ω·m and 0.10 m, and its derating factor $C_{s}$ = 0.705 (Surface layer and Cs, Example 1).

Body current by Eq. (1) and Eq. (2):

I_{B, 50} = \frac{0.116}{0.5} = 0.164 A, I_{B, 70} = \frac{0.157}{0.5} = 0.222 A

Tolerable touch voltage by Eq. (3):

E_{touch50} = (1000 + 1.5 \times 0.705 \times 3000) \frac{0.116}{0.5} = 685 V

Tolerable step voltage by Eq. (4):

E_{step50} = (1000 + 6 \times 0.705 \times 3000) \frac{0.116}{0.5} = 2246 V

Result The mat of the default project is designed to a tolerable touch voltage of 685 V and a tolerable step voltage of 2246 V. For a person of 70 kg the limits are 927 V and 3040 V.

Sources

[1]IEEE Std 80-2013, IEEE Guide for Safety in AC Substation Grounding. §5.3, Eq. 6; §5.3, Eq. 7; §8.3, Eq. 32; §8.3, Eq. 29.

CitationSubstationLayout Reference, Tolerable body current, revision 1, 8 Nov 2026, https://substation.solarlayout.app/library/reference/tolerable-body-current

Tolerable body current

1The current a body toleratesCopy link to The current a body tolerates

2From current to voltageCopy link to From current to voltage

1The current a body tolerates

2From current to voltage