Last updated: May 24, 2026

📐 Quick Reference: Formulas & Cheat Sheets

Bookmark this page. Every formula, ratio, and table used across CalcHub's 98 calculators in one printable reference. Print-friendly CSS included — saves cleanly without nav/footer. Updated when underlying rules change (e.g., new tax brackets).

💰 Financial Formulas

Compound Interest

A = P × (1 + r/n)^(n × t)

A = final amount, P = principal, r = annual rate (decimal), n = compounding periods per year, t = years.

Quick Rule of 72: Years to double money ≈ 72 ÷ rate. At 6% → 12 years. At 9% → 8 years.

Monthly Mortgage Payment

M = P × (r/12) × (1 + r/12)^n / ((1 + r/12)^n − 1)

M = monthly P&I payment, P = principal, r = annual rate (decimal), n = total months.

Example: $300K @ 7% for 30 yrs (360 mo): M = $1,996.

ROI (Return on Investment)

ROI = (Gain − Cost) / Cost × 100%

For multi-year ROI, use CAGR for fair comparison:

CAGR = (End/Start)^(1/years) − 1

2026 US Federal Tax Brackets (Single Filer)

Rate	Taxable Income
10%	$0 – $11,925
12%	$11,926 – $48,475
22%	$48,476 – $103,350
24%	$103,351 – $197,300
32%	$197,301 – $250,525
35%	$250,526 – $626,350
37%	$626,351+

Standard deduction 2026 single: $14,600. Married filing jointly: $29,200.

50/30/20 Budget Rule

50% Needs: rent/mortgage, utilities, groceries, insurance, minimum debt
30% Wants: dining out, subscriptions, hobbies, travel
20% Savings + Debt Payoff: emergency fund, retirement, extra debt principal

Percentages of after-tax (take-home) income, not gross.

2026 Retirement Contribution Limits

Account	Standard	Catch-Up (50+)
401(k) / Roth 401(k)	$23,000	+$7,500
Traditional / Roth IRA	$7,000	+$1,000
HSA (self-only)	$4,300	+$1,000 (age 55+)
HSA (family)	$8,550	+$1,000 (age 55+)
FSA	$3,300	N/A
Total 401(k) (incl. match + after-tax)	$69,500	+$7,500

❤️ Health & Fitness

BMI Categories (WHO Adult)

BMI	Category
< 18.5	Underweight
18.5 – 24.9	Normal weight
25.0 – 29.9	Overweight
30.0 – 34.9	Obese Class I
35.0 – 39.9	Obese Class II
≥ 40.0	Obese Class III

BMI = weight(kg) / [height(m)]² OR 703 × weight(lb) / [height(in)]²

Heart Rate Zones (Karvonen Method)

HRmax = 208 − (0.7 × age) HRR = HRmax − Resting HR Target HR = (HRR × zone%) + Resting HR

Zone	% HRR	Purpose
1 — Recovery	50–60%	Active recovery, warmup
2 — Fat burn	60–70%	Aerobic base building
3 — Aerobic	70–80%	Endurance, cardiovascular fitness
4 — Anaerobic	80–90%	Threshold training
5 — Max	90–100%	HIIT, sprints

TDEE Activity Multipliers

Level	Multiplier	Description
Sedentary	1.2	Office job, no exercise
Light	1.375	Light exercise 1-3 days/wk
Moderate	1.55	Moderate exercise 3-5 days/wk
Very Active	1.725	Hard exercise 6-7 days/wk
Extreme	1.9	Physical job + daily training

TDEE = BMR × Activity Multiplier

🏠 Real Estate Ratios

28/36 Rule (Mortgage Qualification)

28%: Housing (PITI) should not exceed 28% of gross monthly income
36%: Total debt payments should not exceed 36% of gross monthly income

FHA loans often allow up to 31/43; conventional qualified mortgages cap at 43% DTI.

Cap Rate (Rental Property)

Cap Rate = Net Operating Income / Property Value × 100%

Typical good cap rates: 4-6% in major coastal cities; 8-12% in lower-cost markets.

🔬 Math & Science

Percentage Quick Reference

Find X% of Y: Y × X/100
X is what % of Y: X/Y × 100
X is X% of what: X / (percent/100)
% change: (New − Old) / Old × 100

Common Unit Conversions

From	To	Multiply by
kg	lb	2.20462
lb	kg	0.45359
°C	°F	× 1.8 + 32
°F	°C	(F − 32) / 1.8
cm	in	0.39370
m	ft	3.28084
km	mi	0.62137
L	gallon (US)	0.26417
cup	mL	236.59

⚡ Energy & Construction Reference

Concrete Volume (Cubic Yards)

Cubic Yards = Length × Width × Depth (all in feet) / 27

Add 10% waste allowance. Round up to nearest 0.25 yard for delivery.

Paint Coverage Reference

Smooth walls: 1 gallon = 350-400 sq ft / coat
Textured walls: 1 gallon = 300 sq ft / coat
Most rooms need 2 coats; light-over-dark: 3 coats
Subtract 21 sq ft per door, 15 sq ft per window

HVAC Efficiency Ratings

AFUE (gas furnace efficiency): 90-98% modern, 60-70% old
SEER (AC efficiency): 14 federal minimum 2026, 22+ top tier
HSPF (heat pump heating): 8.8 federal minimum, 11+ cold-climate
EER (room AC): 10-15 typical

📚 More References

For complete definitions of all terms used here, visit our 135-term Glossary. For step-by-step methodology on any calculation, see our blog (30 deep-dive guides).

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