All Formulas & Citations
Last reviewed: May 19, 2026
This page lists every formula used in CalQpro calculators, organized by category, with the authoritative source cited for each one. It exists for two reasons: so you can verify the math yourself, and so professionals — riggers, lighting designers, accountants, students, healthcare workers — have a single reference to bookmark.
Every formula here is rendered exactly as it appears on the calculator's own page. If a calculator's formula on this page disagrees with what the tool actually computes, that's a bug — please let us know. We currently publish 30 formulas across 4 categories.
For background on how we research, implement, and verify each formula, see our methodology page.
Live Events
Lighting, audio, video, and rigging formulas for live event production. Sources include the National Electrical Code, ANSI/ESTA rigging standards, IEC audio standards, AES acoustics references, and the Art-Net specification.
Festival Lighting Power Load Calculator
Total amperage, per-leg loading, and generator sizing for a festival lighting rig on single- or three-phase service.
Three-phase: L-N amps = leg_watts / (V_LL/√3 × PF) ; L-L amps = pair_watts / (V_LL × PF) ; Leg total = |phasor sum of L-N + touching L-L| ; Service = worst_leg / 0.80 ; Generator = kVA / 0.80 ; Neutral = √(imbalance² + harmonic²)
Single-phase: I = P / (V × PF) ; Service = I / 0.80 ; kVA = kW / PF ; Generator = kVA / 0.80
- P_fixture = Watts per fixture (from spec sheet)
- PF = Power factor (LED ~0.95, magnetic ballast ~0.85)
- V_LL = Line-to-line service voltage (208 V for 3-phase festival service)
- V_LL/√3 = Line-to-neutral voltage (per leg, ~120 V on 208V service)
- 0.80 = NEC 80% continuous-load rule — applied to the breaker and the generator alike
- kVA = Apparent power = real power (kW) ÷ power factor — what distros and gennies are rated in
- L-L amps = 208V line-to-line load current — carried by BOTH legs of its pair (motors, 208V video/distro)
- Leg total = Phasor (vector) sum of a leg's line-to-neutral and line-to-line currents at their voltage angles. Balanced delta → √3 · I_pair, not 2 · I_pair.
- imbalance = Fundamental neutral current from L-N loads: √(I₁²+I₂²+I₃² − I₁I₂ − I₂I₃ − I₃I₁)
- harmonic = Triplen-harmonic neutral current from non-linear LED loads: k × avg leg current (k ≈ 0 linear, 0.25 mixed, 0.6 non-linear)
LED Wall Power Consumption Calculator
Total wattage, amperage, and required service size for an LED video wall.
P_total = P_panel × N × (brightness%) ; I = P_total / (V × √3 for 3-phase) ; Service = I_peak / 0.80
- P_panel = Maximum watts per panel from manufacturer spec
- N = Total panel count
- V = Service voltage (120, 208, 240, 277, or 480 V)
- 0.80 = NEC 80% continuous-load rule (Article 210.20)
Cable Voltage Drop Calculator (NEC 3% Rule)
Voltage drop across a feeder run given conductor size, length, and load — checks against the NEC 3% recommendation.
V_drop = (factor × K × I × L) / CMA
- factor = 2 for single-phase, √3 for 3-phase
- K = Resistance constant: 12.9 (copper), 21.2 (aluminum)
- I = Load current in amps
- L = One-way distance in feet
- CMA = Circular mil area of conductor (AWG-specific)
Truss Load Calculator (Working Load Limit)
Working Load Limit check for an entertainment truss with the industry-standard 10:1 safety factor.
WLL_actual = WLL_chart × (10 / SF) ; utilization% = total_load / WLL_actual × 100
- WLL_chart = Working Load Limit from manufacturer at this span
- SF = Safety factor (10:1 industry standard for entertainment)
- total_load = Sum of all point loads (lights, motors, video)
Source: ANSI E1.2-2012 — Entertainment Technology Aluminum Trusses
Bridle Calculator (Two-Point Rigging Math)
Leg tensions for a two-point bridle from horizontal span, vertical drop, and load weight.
T_A = W · X₂ · L_A / (V · H) ; T_B = W · X₁ · L_B / (V · H)
- H = Horizontal distance between the two overhead attachment points
- V = Vertical drop from attachment plane to the bridle apex (pickup)
- X₁ / X₂ = Horizontal distance from point A / B to the apex
- L_A / L_B = Leg lengths = √(X² + V²)
- W = Total load weight at the apex
- T_A / T_B = Tension in each leg
DMX Universe Planner Calculator
Number of DMX universes needed for a given channel count, with optional headroom per universe.
universes = ⌈total_channels / (512 − reserved)⌉
- 512 = DMX channels per universe
- reserved = Channels held back per universe (buffer/effects)
- ⌈ ⌉ = Round up to next whole universe
Source: USITT DMX-512 Standard
Art-Net Bandwidth Calculator (DMX over Ethernet)
Network bandwidth consumed by a given universe count and refresh rate on Art-Net.
bytes/s = universes × refresh_Hz × (512 + 30 overhead)
- 512 = DMX channels per universe (one byte each)
- 30 = UDP/IP/Ethernet overhead per packet
- refresh_Hz = Art-Net refresh rate (max 44 Hz per spec)
RT60 Reverb Time Calculator (Sabine Equation)
Reverberation time in a room from volume, surface area, and average absorption coefficient.
RT60 = 0.161 × V / A ; A = surface_area × absorption_coeff
- V = Room volume in m³
- A = Total absorption (sabines)
- absorption_coeff = 0-1, average across all surfaces
Speaker SPL at Distance Calculator (Inverse Square Law)
Sound pressure level at any distance from a point-source speaker given its 1-meter reference.
SPL(d) = SPL(1m) − 20 × log₁₀(d / 1m)
- SPL(d) = Sound pressure level at distance d (dB)
- SPL(1m) = Speaker rated SPL at 1 meter (dB, manufacturer spec)
- d = Distance from speaker, in meters
- −6 dB = SPL drop per doubling of distance (the "rule of thumb")
Speaker Delay & Time Alignment Calculator
Delay time in milliseconds (and samples) for aligning a delay tower to the mains based on distance and air temperature.
delay_ms = (distance_m / c) × 1000 ; c = 331.4 + 0.6 × T(°C)
- c = Speed of sound (m/s) — varies with temperature
- T = Air temperature in °C
- samples = delay_ms × sample_rate / 1000
Subwoofer Array Spacing Calculator (Cardioid, Endfire)
Inter-sub spacing and delay for endfire or cardioid sub arrays tuned to a center frequency.
λ = c / f ; endfire_spacing = λ/4 ; cardioid_spacing = λ/2
- λ = Wavelength at the center frequency (meters)
- c = Speed of sound (343 m/s)
- f = Center frequency to tune for (Hz)
- delay = Inter-sub delay (ms) = spacing / c × 1000
dB Addition Calculator (Combining Sound Sources)
Total SPL when two or more sound sources play together — uses logarithmic addition, not simple sum.
L_total = 10 × log₁₀( Σ 10^(L_i / 10) )
- L_i = Each individual sound level in dB
- L_total = Combined total level in dB
Source: OSHA — Combining Noise Levels
Frequency to Wavelength Calculator (Sound)
Wavelength of a sound frequency in air or water, temperature-corrected.
λ = c / f ; c_air = 331.4 + 0.6 × T(°C) ; c_water = 1480 m/s
- λ = Wavelength (meters)
- c = Speed of sound in the medium (m/s)
- f = Frequency (Hz)
- T = Temperature (°C, for air only)
Phantom Power Load Calculator (Console Budget)
Total phantom-power current draw for a set of condenser mics versus a console power budget.
total_mA = Σ(mA_per_mic × count) ; budget_pct = total_mA / console_max × 100
- mA_per_mic = Current draw per condenser (from spec sheet)
- console_max = Total phantom budget across all channels (typical 200-500 mA)
BPM to Delay Time Calculator (ms) — All Note Divisions
Delay times in milliseconds (and LFO Hz) for every note division at a given BPM, including dotted and triplet variants.
quarter_note_ms = 60,000 / BPM ; dotted = ×1.5 ; triplet = ×(2/3) ; LFO_Hz = 1000 / ms
- BPM = Beats per minute (tempo)
- 60,000 = Milliseconds per minute
- dotted = A dotted note adds half its own value (1.5×)
- triplet = Three notes in the time of two (2/3×)
Source: Sweetwater — BPM and Delay Times
Pixel Pitch & Viewing Distance Calculator (LED Wall)
Minimum, optimal, and maximum viewing distance for an LED wall based on pixel pitch.
d_min (m) ≈ pitch (mm) × 1 ; d_optimal ≈ pitch × 2 ; d_max ≈ pitch × 10
- pitch = Center-to-center distance between adjacent LEDs, in millimeters
- d_min = Minimum distance for no visible pixelation
- d_optimal = Best immersion-to-clarity tradeoff
- d_max = Beyond this, pixel resolution is wasted
Projection Throw Distance Calculator
Projector placement distance for a given screen width and lens throw ratio.
throw_distance = throw_ratio × screen_width
- throw_ratio = Lens specification (e.g. 1.5 for a 1.5:1 lens)
- screen_width = Width of the projected image
- screen_height = screen_width ÷ aspect_ratio
- lumens = ≈ 50 ANSI lumens per ft² for moderate ambient light
Projector Lumens for Venue Calculator
Required projector brightness in ANSI lumens for a given screen area, ambient light, and screen gain.
lumens = (screen_area_ft² × lumens_per_ft²) / screen_gain
- lumens_per_ft² = Required brightness based on ambient: dark 12, low 25, moderate 50, high 100
- screen_gain = 1.0 neutral, 1.3 high-gain, 0.9 ambient-rejecting
Finance
The amortization, compound-interest, and return-on-investment formulas behind our finance tools. Sources are the Consumer Financial Protection Bureau and the SEC.
Mortgage Calculator with Extra Payments
Standard mortgage payment from principal, rate, and term using the annuity formula.
M = P × [r(1+r)^n] / [(1+r)^n − 1]
- M = Monthly payment
- P = Loan principal (amount borrowed)
- r = Monthly interest rate (annual rate ÷ 12 ÷ 100)
- n = Total number of monthly payments (years × 12)
Loan Calculator with Amortization Schedule
Monthly payment for any installment loan (auto, personal, student) using the standard amortization formula.
M = P × [r(1+r)^n] / [(1+r)^n − 1]
- P = Loan amount
- r = Monthly rate (APR ÷ 12 ÷ 100)
- n = Number of monthly payments
Compound Interest Calculator with Monthly Contributions
Future balance of an account with an initial deposit, recurring monthly contributions, and compounding interest.
A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) / (r/n)]
- A = Final balance
- P = Initial principal
- r = Annual interest rate (decimal)
- n = Compounding frequency per year
- t = Time in years
- PMT = Monthly contribution
Debt Payoff Calculator
Number of months to pay off a balance given a fixed monthly payment and APR.
n = −ln(1 − (P × r) / M) / ln(1 + r)
- n = Months to payoff
- P = Balance
- r = Monthly rate (APR ÷ 12 ÷ 100)
- M = Monthly payment
ROI Calculator
Return on investment as a percentage of the original cost.
ROI = (Final Value − Initial Cost) ÷ Initial Cost × 100
- Final Value = Value at end of investment
- Initial Cost = Amount originally invested
Math
Foundational arithmetic and number-theory formulas. Cross-checked against Khan Academy.
Percentage Calculator
Three standard percentage operations: a percent of a number, what percent one number is of another, and percent change.
What is X% of Y: result = (X ÷ 100) × Y
X is what % of Y: result = (X ÷ Y) × 100
Percent change from X to Y: result = ((Y − X) ÷ |X|) × 100
- X / Y = The two input numbers — meaning depends on which mode you pick
Source: Khan Academy — Percent Problems
Percentage Change Calculator
Percent increase or decrease between an original and new value.
% Change = ((New − Old) / |Old|) × 100
- New = The new value
- Old = The original value
Source: Khan Academy — Percent Change
GCF & LCM Calculator
Greatest Common Factor (Euclidean algorithm) and Least Common Multiple of two integers.
GCF × LCM = A × B
- GCF = Greatest Common Factor (via Euclidean algorithm)
- LCM = Least Common Multiple = A × B / GCF
Source: Khan Academy — GCF & LCM
Square Root Calculator
Square root, cube root, or any n-th root of a number via the exponent identity.
ⁿ√x = x^(1/n)
- x = The number
- n = The root index (2 = square, 3 = cube)
Health
Body-composition and metabolic-rate formulas used by our health calculators. Sources are the CDC, the Mifflin-St Jeor 1990 paper, and the US Department of Defense.
BMI Calculator
Body Mass Index from weight and height, in metric or imperial units.
Metric: BMI = weight (kg) ÷ height² (m²)
Imperial: BMI = (weight (lbs) × 703) ÷ height² (in²)
- weight (kg) = Body weight in kilograms
- height (m) = Height in meters
Source: CDC — About Adult BMI
BMR Calculator (Mifflin-St Jeor)
Basal Metabolic Rate — daily calories burned at rest — using the Mifflin-St Jeor equation.
BMR = 10W + 6.25H − 5A + S
- W = Weight in kg
- H = Height in cm
- A = Age in years
- S = +5 for men, −161 for women
Source: Journal of the American Dietetic Association — Mifflin-St Jeor vs Harris-Benedict
Body Fat Calculator (US Navy Method)
Body fat percentage from circumference measurements using the US Navy / DoD formula.
Men: %BF = 86.010 × log₁₀(waist − neck) − 70.041 × log₁₀(height) + 36.76
Women: %BF = 163.205 × log₁₀(waist + hips − neck) − 97.684 × log₁₀(height) − 78.387
- waist, neck, hips = All measurements in inches
- height = Height in inches
Source: DoD — Body Composition Standards
How we cite our work
For every calculator on CalQpro, we identify the canonical published formula and the strongest available authoritative source for it — government code (NEC, CDC, IRS), professional standards bodies (ANSI, ESTA, IEC, AES, AVIXA), peer-reviewed papers, or industry-recognized reference data — and we display that citation next to the formula on the calculator's page.
If you spot a citation that should be stronger, a formula that should be updated against a newer revision, or math that doesn't match a credible third-party reference, let us know via the contact page. We respond within two business days and ship corrections within a week.
For the full process — research, implementation, automated testing, manual cross-verification, and ongoing maintenance — read our methodology page.