Percentage Increase Calculator
Work out a percentage increase or decrease, calculate the percentage change between two values, find a percentage of a number, or add and remove UK VAT — all in one tool with a transparent calculation trail you can verify by hand.
Worked examples sourced from ONS, HMRC and the Bank of England · GBP figures formatted for en-GB.
Calculate a Percentage
The original number (e.g. 50)
The percent uplift (e.g. 10 for a 10% increase)
How to Use This Calculator
Pick a mode
Choose Percentage Increase or Decrease as the primary mode, or switch to % Change, % of, what % is, or Add / remove VAT for the related cases.
Enter your two values
Type the starting value and the percentage (or the two values you are comparing). Decimals and comma-separated thousands such as 1,234.56 are accepted.
Read the result and the trail
The headline figure is shown alongside a green increase or red decrease badge. Underneath, the substituted formula lets you verify the maths by hand.
Percentage Formulas Explained
1. Percentage Increase
New = Old × (1 + p / 100)50 increased by 10% = 50 × 1.10 = 55. The increase itself is 5.
2. Percentage Decrease
New = Old × (1 − p / 100)200 decreased by 25% = 200 × 0.75 = 150. The decrease itself is 50.
3. Percentage Change between two values
Change = ((New − Old) / |Old|) × 100From 80 to 100 = ((100 − 80) / 80) × 100 = +25%. From 100 to 75 = −25%.
4. What is X% of Y?
Result = (X / 100) × Y20% of £1,500 = (20 / 100) × 1,500 = £300 (this is also 20% UK VAT on a net £1,500).
5. X is what % of Y?
Percent = (X / Y) × 10030 out of 120 = (30 / 120) × 100 = 25%.
6. Add or remove VAT
Gross = Net × (1 + p / 100); Net = Gross / (1 + p / 100)£85 net + 20% VAT = £102.00 gross. £120 gross / 1.20 = £100.00 net.
Three things worth remembering:
- A percentage is a decimal multiplied by 100 — 25% is just 0.25 written differently.
- Percentage results can exceed 100% (e.g. a tripling is +200%) and they can be negative (e.g. −25% means a quarter has been lost).
- Division by zero is undefined, so the original or whole value must not be zero in the % change and what% modes.
UK Worked Examples
NHS pay uplift 2026/27 (Band 5 nurse, England)
A Band 5 nurse in England earning £31,049 receives a 3.3% Agenda for Change consolidated uplift on 1 April 2026. The DHSC has published 3.6% for 2025/26 and 3.3% for 2026/27 (Scotland: 4.25% / 3.75%).
£31,049 × (1 + 3.3 / 100) = £31,049 × 1.033 = £32,074.62New salary: £32,073.62 · Increase: £1,024.62
Crossing into the higher-rate band: a 100% jump in marginal tax
When taxable income crosses the higher-rate threshold (£50,270 in 2025/26, frozen to April 2031 per the Autumn Budget 2025), the marginal Income Tax rate doubles from 20% to 40%. The base tax bill on the new pound earned increases by 100%.
((40 − 20) / 20) × 100 = (20 / 20) × 100 = 100%Marginal-rate increase: +100% — exactly why search volume for "what is a 100% increase" spikes around payroll changes.
UK CPI year-on-year change (March 2025 vs March 2024)
The Office for National Statistics publishes Consumer Prices Index annual change as ((index_t − index_{t−12}) ÷ index_{t−12}) × 100. If the CPI All Items index moves from 133.8 to 138.5, the YoY inflation rate is calculated as below.
((138.5 − 133.8) / 133.8) × 100 = (4.7 / 133.8) × 100 = 3.51%YoY CPI change: +3.51% — the canonical ONS year-on-year formula.
A 25 basis-point cut from 4.00% to 3.75% (December 2025 MPC)
The Monetary Policy Committee cut Bank Rate by 25 basis points on 18 December 2025, taking it from 4.00% to 3.75%. This is NOT a 25% cut — it is a 25 bp = 0.25 percentage-point drop. The relative percentage change of the rate itself is calculated below.
((3.75 − 4.00) / 4.00) × 100 = (−0.25 / 4.00) × 100 = −6.25%Absolute drop: −0.25 percentage points (25 bp) · Relative change: −6.25%.
UK VAT add and remove on a £85 net invoice
A self-employed UK trader issues an invoice with a net price of £85 and the standard 20% VAT rate (HMRC, in force since 4 January 2011). Adding VAT gives the customer-facing gross price; removing VAT recovers the net from a VAT-inclusive headline figure.
Add: £85 × 1.20 = £102.00 gross (VAT £17.00). Remove: £120 ÷ 1.20 = £100.00 net (VAT £20.00).Add VAT result: £102.00 gross · Remove VAT result: £100.00 net.
Common Percentages Reference
| Percentage | Decimal | Fraction | UK note |
|---|---|---|---|
| 5% | 0.05 | 1/20 | UK reduced VAT rate |
| 10% | 0.10 | 1/10 | — |
| 15% | 0.15 | 3/20 | — |
| 20% | 0.20 | 1/5 | UK standard VAT rate |
| 25% | 0.25 | 1/4 | — |
| 33.33% | 0.3333 | 1/3 | — |
| 50% | 0.50 | 1/2 | — |
| 75% | 0.75 | 3/4 | — |
| 100% | 1.00 | 1/1 | — |
| 150% | 1.50 | 3/2 | — |
Percentage Points vs Percent vs Basis Points
One of the most common errors when reading UK financial coverage is conflating percentage points, relative percent, and basis points. They look similar but they measure different things.
- Percentage points (pp) — the absolute difference between two percentages. Going from 20% to 25% is a 5 percentage-point increase.
- Relative percent (%) — the same change expressed as a percent of the original. From 20% to 25% is a 25% relative increase, because (25 − 20) ÷ 20 × 100 = 25.
- Basis points (bp) — finance shorthand for one hundredth of a percentage point. 1 bp = 0.01 percentage points, so 100 bp = 1 percentage point. Used by the Bank of England and the Financial Conduct Authority to quote interest-rate moves precisely without the percent / percentage-point ambiguity.
Practical test: when the BoE cuts Bank Rate from 4.00% to 3.75% it is a 25 bp = 0.25 percentage-point cut, but only a 6.25% relative cut. Both sentences are correct; confusing the two is what produces the “25% rate cut” headline error.
Related Concepts
Basis points (bp)
A finance unit equal to 0.01 percentage points. Used by the Bank of England and the FCA so interest-rate moves are unambiguous.
CAGR (Compound Annual Growth Rate)
For multi-year growth: ((end / start)^(1 / years) − 1) × 100. Different from a simple % change, which assumes a single period.
Real vs nominal change
A 5% pay rise when CPI is 3% is roughly a 2% real-terms increase. Connects the headline pay number to ONS inflation.
Year-on-year vs year-to-date
YoY compares the same period across years (the ONS CPI standard). YTD compares this year's accumulated value against the start of this year. They are not interchangeable.
Percentage points vs percent
20% to 25% is a 5 percentage-point increase OR a 25 percent relative increase. Both are correct; users routinely confuse them.
Frequently Asked Questions
What is a 10% increase from 50?
A 10% increase from 50 is 55. The formula is start × (1 + percent ÷ 100), so 50 × 1.10 = 55. The increase itself — the difference between the old and new figures — is 5.
How do I calculate percentage increase?
For a known starting value and a known new value, percentage increase is ((new − old) ÷ old) × 100 when the result is positive. For example, going from 80 to 100 is ((100 − 80) ÷ 80) × 100 = 25%. If you instead know the starting value and the percent uplift, multiply the start by (1 + percent ÷ 100).
What is the difference between percentage increase and percentage decrease?
Percentage increase and decrease share one underlying formula: percentage change = ((new − old) ÷ |old|) × 100. A positive result is an increase, a negative result is a decrease. They are not separate calculations — the sign of the result tells you the direction.
Can a percentage change be negative?
Yes. A negative percentage change indicates a decrease from the original value. For example, a fall from 100 to 75 is a −25% change. Percentage change values can also exceed 100% in either direction (a doubling is +100%, a tripling is +200%, a complete loss is −100%).
How do I find the percentage change between two numbers?
Subtract the old value from the new value, divide by the absolute value of the old, then multiply by 100: ((new − old) ÷ |old|) × 100. The absolute value protects the sign of the result when the starting figure itself is negative, so the percentage tracks the direction of the change rather than the sign of the base.
What is the formula for percentage increase?
New = Old × (1 + p ÷ 100), where p is the percent rise. Rearranged, the percent rise itself is p = ((new − old) ÷ old) × 100. Both forms appear in UK textbooks and in ONS year-on-year change calculations.
How do I calculate UK VAT at 20%?
To add VAT to a net amount, multiply by 1.20: gross = net × 1.20. To remove VAT from a gross figure, divide by 1.20: net = gross ÷ 1.20. The standard UK VAT rate has been 20% since 4 January 2011 (HMRC). Items at the reduced rate use 1.05 / 0.05 in the same formulas.
What does "25 basis points" mean for the Bank of England base rate?
25 basis points equals 0.25 percentage points. A cut from 4.00% to 3.75% is a 25 basis-point cut, NOT a 25% cut. As a relative percentage change of the rate itself, it is ((3.75 − 4.00) ÷ 4.00) × 100 = −6.25%. Confusing percentage points with relative percent is one of the most common mistakes when reading UK monetary-policy headlines.
Authoritative Sources
- ONS — Consumer Prices Indices Technical Manual (2019)UK national statistics body; canonical source for the year-on-year percentage-change methodology.
- ONS — Consumer Prices Indices Technical GuidanceCompanion guidance to the technical manual; conventions used in CPI publication tables.
- HMRC / GOV.UK — VAT ratesStatutory UK tax authority; standard 20%, reduced 5%, zero 0% with the official itemised lists.
- HMRC / GOV.UK — Income Tax rates and Personal AllowancesPersonal Allowance £12,570 and basic / higher / additional rate thresholds for the 2025/26 tax year.
- Bank of England — Bank Rate explainerUK central bank; explains how Bank Rate decisions are quoted in basis points and how they propagate.
- MoneyHelper — Interest rates explainedFCA-backed, UK government-sponsored consumer finance guidance.
- ECMA-402 — Intl.NumberFormat specificationWeb platform standard powering the en-GB number and GBP currency rendering used on this page.
About This Calculator
This UK percentage calculator is provided for general informational and educational purposes. The mathematics is universal, and worked examples reference UK regulator statistics (ONS, HMRC, Bank of England) at the time of writing. For binding tax, insurance or financial decisions, please verify the current rates with the relevant authority or speak to a qualified professional.
Reviewed by Kalcify Editorial Team · Last updated
Reviewed in-house against official tax authority publications, WHO classifications, and primary regulatory sources. We update calculators when underlying rates or rules change.
Published by Kalcify · Data verified against official sources · Learn more about our methodology
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