Formulas and conversions
Quick reference
The formulas that show up at Level I. They are in Ugly’s, but knowing them by heart saves minutes.
Ohm’s law and power
| Find | Formula |
|---|---|
| Voltage | E = I × R |
| Current | I = E ÷ R · I = P ÷ E |
| Resistance | R = E ÷ I |
| Power | P = E × I · P = I² × R · P = E² ÷ R |
Circuits
| Series | Parallel | |
|---|---|---|
| Total resistance | RT = R1 + R2 + … | 1/RT = 1/R1 + 1/R2 + …; two resistors: (R1 × R2) ÷ (R1 + R2) |
| Current | The same everywhere in the circuit | IT = I1 + I2 + … (that is why NAC current is the sum of its appliances) |
| Voltage | Divides: ET = E1 + E2 + … | The same across each branch |
Voltage drop (2-wire DC or single-phase circuit)
- Ugly’s method:
VD = (2 × K × I × L) ÷ CM, with K = 12.9 (copper) or 21.2 (aluminum), L = one-way length (ft) and CM = conductor circular mils. - Resistance method (NEC Chapter 9, Table 8):
VD = I × (Ω/kft × 2 × L ÷ 1000). - Voltage at the last appliance = source voltage − VD. Compare it with the appliance’s listed operating range (for example 16–33 VDC for regulated 24 V appliances).
- Three-phase:
VD = (1.732 × K × I × L) ÷ CM.
| AWG (uncoated copper) | Circular mils | Ω/kft solid | Ω/kft stranded |
|---|---|---|---|
| 18 | 1,620 | 7.77 | 7.95 |
| 16 | 2,580 | 4.89 | 4.99 |
| 14 | 4,110 | 3.07 | 3.14 |
| 12 | 6,530 | 1.93 | 1.98 |
| 10 | 10,380 | 1.21 | 1.24 |
Values from NEC Chapter 9, Table 8 (uncoated copper conductors at 75 °C).
Batteries (secondary power)
Ah = (Istandby × 24 h) + (Ialarm × 5 min ÷ 60), then multiply by the safety margin the design or the code requires (see the Electricity guide). Convert mA to A before multiplying.
Useful conversions
| Inches ↔ feet | 1 ft = 12 in. · 42 in. = 3 ft 6 in. · 80 in. = 6 ft 8 in. · 96 in. = 8 ft |
| Metric | 1 in. = 25.4 mm · 1 ft = 0.3048 m · 1 m = 3.281 ft |
| Temperature | °F = °C × 9/5 + 32 · °C = (°F − 32) × 5/9 |
| Current | 1 A = 1,000 mA · 150 mA = 0.150 A |
| 4:1 ladder | Distance from the base to the wall = working length ÷ 4 |
| Drawing scales | 1/8 in. = 1 ft → 1 in. on the drawing = 8 ft · 1/4 in. = 1 ft → 1 in. = 4 ft |
Practice for the real thing. Take the free 20-minute Level I practice exam (no account needed), or get lifetime access to 85-question exams in the NICET format and 552 Level I questions with explanations.
More NICET Fire Alarm study guides
- 8-week study plan
- Fundamentals and Definitions
- Initiating Devices
- Notification Appliances
- Circuits, Systems, and Control Functions
- NEC 2020 (NFPA 70): Article 760 and Wiring Methods
- Basic Electricity and Calculations
- Inspection, Testing and Maintenance
- Troubleshooting, Repair and Device Replacement
- Job Site Safety: OSHA 1910/1926 and First Aid
- Technical Documents, Drawings, and Submittals
- Community-Reported Topics
- Level I tabbing guide for your printed code books
- Strategy with printed code books
- Key numbers (NFPA 72 · NEC · OSHA)
- Formulas and conversions
- Fire alarm glossary for the NICET exams