Percentage Rate Base Calculator | Find P, R & B

  • Adam
  • November 13, 2025

Free percentage rate base calculator. Find percentage (part), rate (percent), or base (whole) using P=R×B formula. Includes examples & step-by-step solutions.

Percentage Rate Base Calculator – Find Percentage, Rate & Base

The percentage rate base calculator solves the fundamental relationship between three interconnected values: percentage (the part), rate (the percent), and base (the whole). Using the formula Percentage = Rate × Base, this calculator finds any missing value when you provide the other two. Whether you need to calculate what percentage 30 is of 150 (rate), find 20% of 500 (percentage), or determine the whole amount when 40 equals 25% (base), this comprehensive tool handles all percentage calculations with step-by-step explanations and real-world examples.

🔢 Find Percentage (Part)

Calculate: What is [Rate]% of [Base]?

Enter the percentage rate
The total or whole amount

Percentage Calculation Result

Percentage (Part)
100
Rate
20%
Base (Whole)
500

Calculation Breakdown

Step Value
Formula Used P = R × B
Rate (as decimal) 0.20
Base 500
Calculation 0.20 × 500
Percentage (Answer) 100

📊 Find Rate (Percent)

Calculate: [Percentage] is what % of [Base]?

The part amount
The total or whole amount

Rate Calculation Result

Rate (Percent)
20%
Percentage (Part)
30
Base (Whole)
150

Calculation Breakdown

Step Value
Formula Used R = (P / B) × 100
Percentage (Part) 30
Base (Whole) 150
Division 30 / 150 = 0.20
Multiply by 100 0.20 × 100
Rate (Answer) 20%

🎯 Find Base (Whole)

Calculate: [Percentage] is [Rate]% of what?

The part amount
Enter the percentage rate

Base Calculation Result

Base (Whole)
160
Percentage (Part)
40
Rate
25%

Calculation Breakdown

Step Value
Formula Used B = P / R
Percentage (Part) 40
Rate (as decimal) 0.25
Calculation 40 / 0.25
Base (Answer) 160

Understanding Percentage, Rate, and Base

Percentage problems involve three interconnected components that form the foundation of all percentage calculations. Understanding the relationship between percentage, rate, and base is essential for solving everyday math problems from calculating discounts and sales tax to understanding test scores and financial statements.

The Three Components

Percentage (P): The part or portion of the whole. It represents the result when you take a certain percent of the base. The percentage is expressed in the same unit as the base—if the base is in dollars, the percentage is in dollars; if the base is students, the percentage is students. It's NEVER expressed as a percent (with the % symbol).

Rate (R): The percent itself, always expressed with the % symbol. It represents what portion the percentage is of the base. The rate tells you "how much per hundred" and is the only value that uses the percent sign.

Base (B): The whole, total, or complete amount. It represents 100% of the quantity being considered. The base is typically preceded by words like "of," "as much as," "as many as," or "out of" in word problems.

The Fundamental Percentage Formulas

Three formulas connect percentage, rate, and base. Each formula is derived from the others:

Formula 1: Finding Percentage (the Part)

Find Percentage When Rate and Base are Known:

Percentage = Rate × Base
P = R × B

Important: Convert the rate from percent to decimal by dividing by 100

Example: Rate = 20% = 0.20 as decimal

Example: What is 20% of 500?

Given: Rate = 20%, Base = 500

Step 1: Convert rate to decimal = 20% ÷ 100 = 0.20

Step 2: Apply formula P = R × B

Step 3: P = 0.20 × 500 = 100

Answer: The percentage (part) is 100

Interpretation: 100 is 20% of 500

Formula 2: Finding Rate (the Percent)

Find Rate When Percentage and Base are Known:

Rate = (Percentage / Base) × 100
R = (P / B) × 100

Important: Multiply by 100 to convert decimal to percent

Example: 30 is what percent of 150?

Given: Percentage = 30, Base = 150

Step 1: Apply formula R = (P / B) × 100

Step 2: R = (30 / 150) × 100

Step 3: R = 0.20 × 100 = 20%

Answer: The rate is 20%

Interpretation: 30 is 20% of 150

Formula 3: Finding Base (the Whole)

Find Base When Percentage and Rate are Known:

Base = Percentage / Rate
B = P / R

Important: Convert rate to decimal before dividing

Example: 40 is 25% of what number?

Given: Percentage = 40, Rate = 25%

Step 1: Convert rate to decimal = 25% ÷ 100 = 0.25

Step 2: Apply formula B = P / R

Step 3: B = 40 / 0.25 = 160

Answer: The base (whole) is 160

Interpretation: 40 is 25% of 160

Memory Triangle Method

A simple triangle diagram helps remember all three formulas:

Triangle Method:

       P
      ───
      R×B

How to use:

  • To find P (Percentage): Cover P → You see R × B below → P = R × B
  • To find R (Rate): Cover R → You see P above, B beside → R = P / B
  • To find B (Base): Cover B → You see P above, R beside → B = P / R

Real-World Examples of Rate, Base, and Percentage

Example 1: Shopping Discount

Problem: A shirt costs $80 (base). The store offers 30% off (rate). How much is the discount (percentage)?

  • Base (B): $80 (original price)
  • Rate (R): 30% (discount rate)
  • Find: Percentage (discount amount)
  • Formula: P = R × B = 0.30 × 80 = $24
  • Answer: The discount is $24. You pay $56.

Example 2: Test Score

Problem: You scored 45 points (percentage) out of 50 total (base). What's your percentage score (rate)?

  • Percentage (P): 45 points (what you earned)
  • Base (B): 50 points (total possible)
  • Find: Rate (your percentage score)
  • Formula: R = (P / B) × 100 = (45 / 50) × 100 = 90%
  • Answer: Your test score is 90%

Example 3: Sales Tax

Problem: You paid $4.50 in sales tax (percentage) at 9% rate. What was the purchase amount (base)?

  • Percentage (P): $4.50 (tax paid)
  • Rate (R): 9% (tax rate)
  • Find: Base (purchase amount)
  • Formula: B = P / R = 4.50 / 0.09 = $50
  • Answer: The purchase amount was $50

Common Percentage Rate Base Problems

Problem Type Example Question Formula Answer
Find Percentage What is 15% of 200? P = 0.15 × 200 30
Find Rate 75 is what % of 300? R = (75/300) × 100 25%
Find Base 18 is 30% of what? B = 18 / 0.30 60
Discount 20% off $75 item P = 0.20 × 75 $15 discount
Tax 8% tax on $150 P = 0.08 × 150 $12 tax
Tip 18% tip on $45 bill P = 0.18 × 45 $8.10 tip
Grade 42 out of 50 points R = (42/50) × 100 84% score

Frequently Asked Questions

What is the formula for percentage, rate, and base?
Three formulas connect these values: 1) Percentage = Rate × Base (P = R × B), 2) Rate = (Percentage / Base) × 100 (R = (P/B) × 100), 3) Base = Percentage / Rate (B = P/R). Example: What is 20% of 500? P = 0.20 × 500 = 100. The percentage is 100. Note: Convert rate to decimal (20% = 0.20) before multiplying. These formulas solve any percentage problem when you know two values and need to find the third.
What is the difference between percentage, rate, and base?
Percentage (P) is the part/portion of the whole, expressed in same units as base (dollars, items, points—never with % symbol). Rate (R) is the percent itself, always with % symbol, shows what portion percentage is of base. Base (B) is the whole/total amount, represents 100%, often follows words "of" or "out of." Example: "30 is 20% of 150"—30 is percentage (part), 20% is rate (percent), 150 is base (whole). Base is what you're taking a percent OF, percentage is the RESULT, rate is the PERCENT used.
How do you find the percentage when given rate and base?
Use formula: Percentage = Rate × Base (P = R × B). Steps: 1) Convert rate from percent to decimal (divide by 100), 2) Multiply decimal rate by base. Example: What is 25% of 80? Step 1: 25% = 25/100 = 0.25. Step 2: P = 0.25 × 80 = 20. Answer: 20. Verification: 20 is 25% of 80 ✓. Real-world: 25% discount on $80 item = $20 off, pay $60. Remember: rate must be decimal before multiplying.
How do you calculate rate when given percentage and base?
Use formula: Rate = (Percentage / Base) × 100. Steps: 1) Divide percentage by base, 2) Multiply result by 100 to get percent. Example: 45 is what percent of 180? Step 1: 45 / 180 = 0.25. Step 2: 0.25 × 100 = 25%. Answer: 25%. Verification: 25% of 180 = 45 ✓. Real-world: Scored 45 out of 60 points = (45/60) × 100 = 75% grade. Remember: multiply by 100 to convert decimal to percent.
How do you find the base when given percentage and rate?
Use formula: Base = Percentage / Rate (B = P / R). Steps: 1) Convert rate to decimal, 2) Divide percentage by decimal rate. Example: 30 is 15% of what number? Step 1: 15% = 0.15. Step 2: B = 30 / 0.15 = 200. Answer: 200. Verification: 15% of 200 = 30 ✓. Real-world: Paid $12 tax at 8% rate, purchase was 12/0.08 = $150. Remember: convert rate to decimal before dividing. Common error: dividing by 15 instead of 0.15.
What are real-life examples of percentage, rate, and base?
Discounts: 30% off (rate) $80 item (base) = $24 discount (percentage). Sales tax: 7% tax (rate) on $50 purchase (base) = $3.50 tax (percentage). Test scores: 42 points (percentage) out of 50 total (base) = 84% grade (rate). Tips: 18% tip (rate) on $60 bill (base) = $10.80 tip (percentage). Salary increase: 5% raise (rate) on $40,000 salary (base) = $2,000 increase (percentage). Interest: 4% rate on $1,000 deposit (base) = $40 interest (percentage). Commission: 6% rate on $5,000 sales (base) = $300 commission (percentage).
How do you identify rate, base, and percentage in word problems?
Look for key phrases: Base follows "of," "out of," "as much as"—it's the whole/total (often larger number). Rate has % symbol or word "percent"—shows what portion. Percentage is the part/result (same units as base, no % symbol). Examples: "What is 20% of 500?"—Rate=20%, Base=500, find Percentage. "30 is what percent of 150?"—Percentage=30, Base=150, find Rate. "40 is 25% of what?"—Percentage=40, Rate=25%, find Base. Tip: Percentage and base have same units (both dollars, both items); only rate has %.

Tips for Solving Percentage Problems

Step-by-Step Problem-Solving Process

  • Step 1 - Identify what's given: Determine which two values you know (P, R, or B)
  • Step 2 - Identify what's missing: Determine which value you need to find
  • Step 3 - Choose the right formula: Use the appropriate formula based on what's missing
  • Step 4 - Convert rate if needed: Change percent to decimal for calculations
  • Step 5 - Calculate: Apply the formula and solve
  • Step 6 - Verify: Check your answer by substituting back into P = R × B

Common Mistakes to Avoid

  • Forgetting to convert rate: Must change 25% to 0.25 before calculating
  • Confusing percentage and rate: Percentage is the answer amount (no %), rate is the percent (%)
  • Using wrong formula: Make sure you're solving for the missing variable
  • Unit mismatch: Percentage and base must have same units
  • Dividing instead of multiplying: To find percentage, multiply rate by base (not divide)

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