Calculator formulas

How to use this guide

Each section matches a calculator and ends with a worked example you can check against it.

Field estimate only. Manufacturer data, the authority having jurisdiction (AHJ), and current applicable code govern material and whether a circuit is energized. See the disclaimer.

Ohm's law and power

Every power calculation in this guide reduces to these four relationships.

V = I × R    I = V ÷ R    R = V ÷ I

P = V × I    P = I² × R    P = V² ÷ R    I = P ÷ V

Voltage drop

Drop is the round trip: two legs of the same gauge, so the one-way length is doubled.

V_drop = (2 × L × I × (R/kft)) ÷ (1000 × n)

V_device = V_{supply reading} − V_drop   % drop = (V_drop ÷ V_supply) × 100

Pass window. Built from the nominal rating, not the meter reading: V_nominal × (1 ± tolerance). At ±10%, 12 VDC is 10.8 to 13.2 V and 24 VDC is 21.6 to 26.4 V.

Room left.

L_max = ((V_supply − V_min) × 1000 × n) ÷ (2 × I × (R/kft))

I_max = ((V_supply − V_min) × 1000 × n) ÷ (2 × L × (R/kft))

Corrections to the table value.

R_T = R₂₀ × [1 + 0.00393 × (T_°C − 20)]

• Stranded class B: table value × 1.02. Fine-strand or tinned: × 1.08.
• Paralleling spare conductors divides loop resistance by n (doubling up in 18/4 halves it).
• AC at these gauges and lengths is treated as purely resistive.
• Measured drop above calculated: implied loop resistance = measured drop ÷ I. Extra resistance points to a bad splice, damaged conductor, CCA or aluminum, or a longer run than entered.

Worked example. 24 VDC supply, 0.5 A maglock, 150 ft of 18 AWG stranded: 2 × 150 × 0.5 × 6.513 ÷ 1,000 = 0.98 V drop, 23.02 V at the device. That is inside 21.6 to 26.4 V. Maximum length is 2.4 × 1,000 ÷ (2 × 0.5 × 6.513) = 368.5 ft.

Voltage drop calculator

Low voltage load and supply sizing

Size the supply to peak current times a headroom factor, one supply and one voltage at a time.

I_row = qty × draw    draw_A = mA ÷ 1000   or   W ÷ V_system

I_peak = Σ I_continuous + Σ I_momentary   I_demand = I_peak × 1.30

Loading % = (I_demand ÷ I_{supply rating}) × 100    P_total = I × V_system

I_charging = (Ah × 1.2) ÷ recharge hours

• Continuous: maglocks, readers, controllers, anything energized while secure.
• Momentary: fail-secure strikes and other devices energized only while released.
• The 1.30 headroom factor is an allowance for charging and growth, not a code requirement. Charging current is a separate line and is not added into demand a second time.

Worked example. Four maglocks at 500 mA = 2.0 A continuous. 2.0 × 1.30 = 2.6 A demand. A 3 A supply carries it at 87% loading; a 2.5 A supply does not.

Low voltage load calculator

AC to DC conversion

A meter reads RMS, a filter capacitor charges to the peak, and each diode in the current path costs a fixed drop.

V_peak = V_RMS × 1.4142    V_RMS = V_peak × 0.7071

V_{DC, filtered} = V_peak − (N_diodes × V_d)

V_{DC, unfiltered full wave} = 0.6366 × V_peak − (N_diodes × V_d)

V_{DC, half wave} = 0.3183 × V_peak − V_d

V_{RMS required} = (V_{DC required} + (N_diodes × V_d)) ÷ 1.4142

V_{unloaded secondary} = V_RMS × (1 + regulation %)

V_{ripple, p-p} ≈ I_load ÷ (f_ripple × C)

Ripple valley = V_DC − V_ripple. A device that needs a minimum DC can fall out of spec at the valley even when the average looks fine.

Worked example. 24 VAC through a silicon bridge and a filter capacitor: 24 × 1.4142 = 33.94 V peak, minus 1.4 V of diode drop = 32.54 VDC with no load. At 10% regulation the unloaded secondary is 26.4 VAC, which reads about 35.9 VDC.

AC to DC conversion calculator

Backup battery and UPS sizing

A panel battery is sized in amp-hours at the 20-hour rating; rack equipment is sized in watts and watt-hours.

Panel battery (12 or 24 VDC)

Ah_required = (I_load × hours) ÷ rate factor    Ah_design = Ah_required × 1.25

I_{charging available} = I_{supply rating} − I_load

recharge hours = (Ah_installed × 1.2) ÷ I_{charging available}

runtime hours = (Ah_installed × rate factor) ÷ I_load

Other durations: use the battery datasheet's discharge table. Capacity also falls with age and cold.

• Batteries in series add voltage, not capacity. Two 12 V 7 Ah batteries are a 24 V 7 Ah bank.
• A 7 Ah battery is 7 Ah over 20 hours and closer to 4 Ah over one hour.
• If available charging current is zero or negative, the supply cannot recharge the battery under load.

Equipment UPS

VA = (W_load × headroom) ÷ power factor

Wh_battery = (W_load × hours) ÷ (efficiency × DoD × derate)

Wh_usable = W_published × hours_published   runtime ≈ Wh_usable ÷ W_load

Inverter efficiency defaults to 0.85. The chart-point estimate is a straight line; runtime falls faster than linear at higher loads, so the manufacturer's runtime chart governs.

Worked example. 24 VDC panel at 3.75 A for 1 hour: 3.75 × 1 ÷ 0.60 = 6.25 Ah, × 1.25 = 7.81 Ah. An 8 Ah battery covers it; a 7 Ah does not. On a 4 A supply, 0.25 A is left for charging, so a 7 Ah battery takes 7 × 1.2 ÷ 0.25 = 33.6 hours to recharge.

UPS and backup battery calculator

Video bandwidth

Start from the H.264 table value at 30 fps, then scale for frame rate, codec, and smart codec.

Mbps_camera = Mbps_{H.264 @ 30 fps} × (fps ÷ 30)^0.75 × codec factor × smart factor

Mbps_group = Mbps_camera × lenses × qty    Mbps_link = Σ Mbps × (1 + headroom)

Mbps_MJPEG = (KB_frame × fps × 8) ÷ 1000

GB/hour = (Mbps × 3600) ÷ (8 × 1000)    GB/day = (Mbps × 86400) ÷ (8 × 1000)

Utilization = traffic with headroom ÷ link speed. Figure recording (cameras to recorder), local viewing, and remote viewing (WAN upload) as three separate segments.

Worked example. 20 cameras at 1080p, 30 fps, H.264, medium activity: 20 × 4.0 = 80 Mbps, or 100 Mbps with 25% headroom. That is 80 × 86,400 ÷ 8,000 = 864 GB per day. On H.265 it is 80 × 0.55 = 44 Mbps.

Video bandwidth calculator

Video storage and RAID

Storage is daily volume times retention, plus overhead, figured per camera group and summed.

GB/day = ((Mbps × 86400) ÷ (8 × 1000)) × recording share

TB_raw = Σ (GB/day × retention days) ÷ 1000    TB_{usable required} = TB_raw × (1 + overhead)

TiB = TB × (1000⁴ ÷ 1024⁴) = TB × 0.9095

retention delivered = (TB_{usable array} ÷ (1 + overhead)) ÷ (TB/day)

A hot spare adds one physical drive that holds no data. Default overhead for file system and VMS database is 10%. Drives are sold in decimal TB; the operating system reports TiB.

Worked example. 864 GB per day for 30 days = 25.92 TB raw. With 10% overhead, 28.5 TB usable required (25.9 TiB). Six 8 TB drives in RAID 6 give (6 − 2) × 8 = 32 TB usable, which holds 32 ÷ 1.1 ÷ 0.864 = 33.7 days.

Video storage calculator

Field of view and DORI

Pixel density sets what a camera can do at a distance; the same pixels spread over a wider scene as distance grows.

HFOV = 2 × arctan(sensor width ÷ (2 × f))

VFOV = 2 × arctan(tan(HFOV ÷ 2) × 9 ÷ 16)

scene width = 2 × D × tan(HFOV ÷ 2) = (D × sensor width) ÷ f

scene height = scene width × 9 ÷ 16

px/ft = horizontal px ÷ scene width_ft    px/m = px/ft × 3.2808

D_level = horizontal px ÷ (threshold_px/ft × 2 × tan(HFOV ÷ 2))

f_needed = (threshold × sensor width × D) ÷ horizontal px

Use the 9/16 ratio for 16:9; use 3/4 for 4:3. With a datasheet angle, use it directly in place of the arctan calculation. Default sensor width is 5.37 mm (typical 1/2.8 in).

Mounting geometry (flat, level ground; h = mounting height):

near edge = h ÷ tan(tilt + VFOV ÷ 2)

center = h ÷ tan(tilt)

far edge = h ÷ tan(tilt − VFOV ÷ 2)

The far edge is unbounded when tilt − VFOV/2 is at or above horizontal. License plates are not a DORI level; they need far more density plus correct lighting, angle, and shutter.

Worked example. 4 mm lens, 5.37 mm sensor, 1920 px: HFOV = 67.7°. At 30 ft the scene is 30 × 5.37 ÷ 4 = 40.3 ft wide, 1920 ÷ 40.3 = 47.7 px/ft (Recognise). Identify reaches 1920 ÷ (76.2 × 1.3425) = 18.8 ft; Detect reaches 187.7 ft.

Field of view and DORI calculator

Conduit fill

Fill is total cable area over conduit internal area, held to the NEC Chapter 9 Table 1 limit for the cable count.

A_cable = π × (OD ÷ 2)² = 0.7854 × OD²

fill % = (Σ (qty × A_cable) ÷ A_conduit) × 100

cables remaining = ((A_conduit × limit) − Σ A) ÷ A_cable

Source: NEC Chapter 9 Table 4. Confirm against the edition your AHJ enforces.

• Jam ratio. Three same-size cables can wedge at a bend when conduit ID ÷ cable OD falls between 2.8 and 3.2.
• Total bends between pull points are commonly held to 360°.
• Use the top of the cable's published OD range unless the datasheet is in hand.

Worked example. 24 Cat6 at 0.250 in OD: 0.0491 sq in each, 1.178 sq in total. In 1-1/2 in EMT that is 1.178 ÷ 2.036 = 57.9%, over the 40% limit. In 2 in EMT it is 1.178 ÷ 3.356 = 35.1%, which passes.

Conduit fill calculator

Cable tray and J-hook capacity

Check area and weight separately; whichever reaches its limit first governs, and above a ceiling that is usually weight.

Area

A_tray = width × loading depth    A_J-hook = π × (opening ÷ 2)²

A_allowed = A_pathway × design fill    max cables = A_allowed ÷ A_cable

bundle depth = Σ A_cable ÷ width

Weight

lb/ft = Σ (qty × lb/kft) ÷ 1000    lb per hook = lb/ft × hook spacing_ft

% of tray rating = (lb/ft ÷ rated lb/ft) × 100    kg/km = lb/kft × 1.488

• Design fill is a design choice (25%, 40%, or 50%), following TIA and BICSI practice and the tray rating. NEC tray fill tables are for power conductors.
• Many installers cap a bundle near 24 cables and dress bundles side by side.
• Support spacing is commonly 4 to 5 ft, independent of the ceiling grid.
• J-hook catalog cable counts govern over the geometric figure.

Worked example. A 12 in × 4 in usable tray is 48 sq in. At 50% fill that allows 24 sq in, about 488 Cat6 at 0.0491 sq in each. At about 28 lb/kft that bundle is 13.7 lb/ft. On J-hooks at 4 ft, each hook carries about 55 lb.

Cable tray and J-hook calculator

Fiber link loss budget

Total loss is fiber length times attenuation, plus every mated pair and every splice.

loss_dB = (L_km × dB/km) + (pairs × dB_pair) + (splices × dB_splice)

power budget = P_Tx − P_{Rx sensitivity}   margin = power budget − loss_dB ≥ 3 dB

km = m ÷ 1000 = ft ÷ 3280.84

• Each patch panel the link passes through is one mated pair. A switch-to-switch link through two panels is two pairs.
• Certification is judged against the TIA maximum. Typical values show what a clean run often reads.
• Dirty end faces are the most common cause of a failed test. Clean and inspect before troubleshooting.

Worked example. 300 m of OM4 at 850 nm, two pairs, one fusion splice: (0.3 × 3.5) + (2 × 0.75) + 0.3 = 2.85 dB maximum. On typical values: 1.05 + 0.6 + 0.1 = 1.75 dB.

Fiber link loss calculator

Subnet and CIDR (IPv4)

The prefix sets the block size; the first address is the network, the last is the broadcast, and everything between is usable.

total addresses = 2^{(32 − prefix)}    usable = total − 2

network = IP AND mask    broadcast = network OR wildcard    wildcard octet = 255 − mask octet

Exceptions: a /31 has 2 usable addresses on a point-to-point link (RFC 3021); a /32 is a single host.

Keep static device addresses outside the DHCP pool, and confirm the plan with IT before addressing cameras or controllers.

Worked example. 192.168.1.0/27: mask 255.255.255.224, 2⁵ = 32 addresses. Network 192.168.1.0, broadcast 192.168.1.31, usable 192.168.1.1 through 192.168.1.30 (30 hosts).

Subnet and CIDR calculator

PoE budget and distance

The switch budget is spent at the class PSE figure, not the sum of device datasheets.

W_reserved = Σ (qty × W_{PSE class})    W_remaining = W_budget − W_reserved

headroom limit = W_budget × 0.80    % of budget = (W_reserved ÷ W_budget) × 100

Cable loss on one run

I = W_PSE ÷ V_PSE    R_loop = (2 × L_ft × (R/kft)) ÷ (1000 × c)

W_loss = I² × R_loop    W_device = W_PSE − W_loss

c = conductors per polarity: 2 on two-pair PoE, 4 on four-pair (802.3bt). V_PSE = 44 V for Type 1, 50 V for Type 2 and above. Copper: 24 AWG 25.67 Ω/kft, 23 AWG 20.36 Ω/kft.

• The 100 m channel (90 m horizontal plus 10 m of cords) is a data limit, not a power limit. Past it, use a PoE extender, a media converter with local power, or fiber with an injector at the far end.
• Port count and watt budget are separate limits. Some switches allocate by class, others by measured draw; the switch datasheet governs.

Worked example. Eight Class 4 cameras reserve 8 × 30 = 240 W. On a 370 W switch that leaves 130 W at 64.9% of budget, inside the 296 W headroom limit. One 90 m run of 24 AWG: I = 30 ÷ 50 = 0.6 A, R_loop = 2 × 295.3 × 25.67 ÷ (1,000 × 2) = 7.58 Ω, loss = 0.6² × 7.58 = 2.73 W, so about 27.3 W reaches the device.

PoE budget and distance calculator

Unit conversions and EOL resistor color code

Resistor value = (first band digit, second band digit) × 10^{(third band)}. Fourth band is tolerance: gold ±5%, silver ±10%.

The required value on a supervised zone comes from the panel documentation.

EOL resistor color code

Sources

• LowVoltKit calculators: formulas, defaults, and worked examples for all twelve calculators
• LowVoltKit EOL resistor color code
• NEC Chapter 9, Tables 1 and 4 (conduit fill limits and internal areas)
• IEEE 802.3af, 802.3at, 802.3bt (PoE classes)
• ANSI/TIA-568 (fiber component allowances, 100 m channel)
• IEC 62676-4 (DORI pixel density levels)
• RFC 1918 and RFC 3021 (private ranges, /31 links)